# Questions on Geometry: Triangles answered by real tutors!

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Question 817299: Explain how you determine the smallest segment of a triangle when give the angles

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the smallest segment of the triangle is the line segment opposite the smallest angle.

Question 817241: if the perimeter of the figure below is 13 meter what it the value of x

Question 817166: Find the area and perimeter of the triangle below where the angle at A is a right angle, AB = 8 inches, BC= 10 inches, and AC = 6 inches
You can put this solution on YOUR website!
Area of a right triangle

b=CB
h=AB

Area=24 sq. in.
Perimeter of a triangle

Perimeter=24 in.

Question 817116: what is the largest area of the circle can be drawn inside a rectangle of length and breadth 21 and 30 respectively?
You can put this solution on YOUR website!
the largest diameter of the circle would be 21
area of a circle is pi*r^2
pi*10.5^2
pi*110.25
346.36059005827470454050643300657

Question 817063: The length of a side of an equilateral triangle is represented by 2x-1. If the perimeter of the triangle is 21, what is the value of x ?
You can put this solution on YOUR website!
All sides are equal
perimeter = 3(2x-1)
3(2x-1)=21
2x-1= 21/3
2x-1=7
2x=7+1
2x=8
x=8/2
x=4

Question 817046: A triangle has side measures of 11 inches and 30 inches. Which of the following is a possible length of the third side?
A. 11 inches
B. 19 inches
C. 27 inches
D. 41 inches

Question 816901: Two Similar Triangles have a scale factor of 2/3. If the longest side of the smaller triangle is 15 inches, determine the length of the longest side of the larger triangle

You can put this solution on YOUR website!
```
Hi,
Two Similar Triangles have a scale factor of 2/3.
If the longest side of the smaller triangle is 15 inches,
determine the length 'x' of the longest side of the larger triangle
|Cross Multiplying to solve

x = 3*15in/2 = 22.5in

```

Question 816854: The hypotenuse of a triangle is 34 cm. If the other two sides add up to 46 cm, then what are their lengths?
You can put this solution on YOUR website!
x+y=46,
x^2+y^2=34^2
x = 30, y = 16
or
x = 16, y = 30

Question 816716: 36 = s + s + (2s - 4) What is the length of the base?
You can put this solution on YOUR website!
```
Hi,
What is the length of the base (2s - 4)?
36 = s + s + 2s - 4
36 = 4s - 4             |Solving for s
40 = 4s
10 = s   and the base is 16
36 = 10 + 10 + 16 = 36
```

Question 816688: ABCD is a square if AB measure 12 3/4 ft. what is the measurement of AD

You can put this solution on YOUR website!
Since ABCD is a square, all side lengths are equal.
AB is a side with length 12 3/4. AD is a side of the square,
so AD has length 12 3/4 .

Question 816545: [ What is the measure of a base angle of an isosceles triangle if the vertex angle measures 46 [degrees] and the two congruent sides each measure 21 units? ]
You can put this solution on YOUR website!
B = (180 - 46)/2
B = 67 degrees
---
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---
---
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Question 816563: if a triangle ABC exists then what is the length of AB if AC=10 BC=6 and the angle ACB= 120 degrees? How do I solve this
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if a triangle ABC exists then what is the length of AB if AC=10 BC=6 and the angle ACB= 120 degrees? How do I solve this
----
The side opposite ---
Use the Law of Cosines to fing AB:
AB^2 = 10^2+6^2-2*10*6*cos(120)
----
AB^2 = 166
AB = 12.88
==================
Cheers,
Stan H.

Question 816364: Determine whether triangle QRS is a right triangle for the given vertices. Explain.
Q(–13, –1), R(–15, –1), S(4, 9)

You can put this solution on YOUR website!

QR is part of the horizontal line .
If QS were a vertical line, the x-coordinate of S would be ,
just like for Q.
If RS were vertical, the x-coordinate for S would be : .
Neither QS nor RS are vertical lines,
so there is no right angle at Q or at R.
Is there a right angle at S?
Without calculating, we see that the length of QR is 2 units,
while QS and RS are much longer,
So the angle at S is the smallest angle, and cannot be a right angle.

NOTES:
Maybe that was not the way your teacher expects you to get to the answer,
but it is the shortest way to the answer.
Maybe there is a typo,
and I just gave you the right answer to the wrong problem.

Question 816326: if the sides of a right triangle are 20 ft (hypotenuse) and 13 ft (a), what is b?
You can put this solution on YOUR website!
```
Hi,
if the sides of a right triangle are 20 ft (hypotenuse) and 13 ft (a), what is b?
Applying Pythagorean Theorem:
b =  = ft
```

Question 814762: The hypotenuse of a right triangle is 17 cm long. Another side of the triangle is 7 cm longer than the third side. Determine the unknown side lengths.
You can put this solution on YOUR website!
Let one side = x cm. Then,
Second side = x + 7 cm.
Hypotenuse = 17 cm. (Given)
According to the Pythagoras theorem,

=
=
=
=
= Dividing this equation by 2, we get
=
=
= . So, either (x+15) or (x-8) = 0.
So, x = -15 or x = 8. But x cannot be equal to -15 as it is not a real No.
So, . So one side = 8 cm. and another side = 15.
I think, it is clear to you now. All the best. Feel free to contact me at gsmani9@yahoo.com as I am a home tutor in India.

Question 815155: one side of a right angle triangle is 20 inches and the hypothesis is 10 inches longer than the other side. find the lengths of the unknown side
You can put this solution on YOUR website!
Let one side = x inches
The second side = 20 inches (Given)
So, the hypotenuse = (x+10) inches. (Given)
As per the Pythagoras theorem,
Hypotenuse =
So, (x+10)^2 =
=
=
=
= So, ; x = 15
So, the unknown side = 15 inches. Answer.
I guess, it is clear to you. God bless you.
Feel free to contact me at gsmani9@yahoo.com if you have any problem. I am a
home tutor in India.

Question 816235: A can do a piece of work in 24 days while B can alone do it in 16 days. With the help of C, they finish the work in 8 days. In how many days can C alone do this work
You can put this solution on YOUR website!
1/24+1/16+1/c=1/8
8/24+8/16+8/c=1
1/3+1/2+8/c=1
2/6+3/6+8/c=1
5/6+8/c=1
8/c=1/6
c=48 days alone
a and b without c
x/24+x/16=1
2x/48+3x/48=1
5x/48=1
x=48/5
x=9.6 days for a and b

Question 816233: If the hypotenuse of a 30–60–90 triangle has length meters, what is the length of the longer leg of the triangle in meters?
You can put this solution on YOUR website!
If the hypotenuse of a 30–60–90 triangle has length ?? meters, what is the length of the longer leg of the triangle in meters?
------
The ratio of the sides is x:2x:sqrt(3)x where 2x is the hypotenuse.
------
If hypotenuse = ??, the shortest side is (1/2)??
----
And the length of the longer side is (sqrt(3))(1/2)?? = (1/2)(sqrt(3)(??)
=========
Cheers,
Stan H.
==============

Question 816227: Area of a square with side x is equal to the area of a triangle with base x. The latitude of a triangle is
You can put this solution on YOUR website!
Area of a square with side x is equal to the area of a triangle with base x. The altitude of a triangle is
-----
Area of square:: x^2
Area of triangle:: (1/2)x*h
-------
Equation:
(1/2)x*h = x^2
xh = 2x^2
-----
h = 2x
-----
altitude of the triangle = 2x
================
Cheers,
Stan H.

Question 815992: Greetings, I am in Trig but i am struggling with old knowledge, Heres the Problem: I am using the law of sines but cant remember how to properly manipulate fractions So if i have Sine A /a = Sine B / b = Sine C / c (this is the law of sines) If i have sine 56 / a = Sine 63 / 12 How do i move the a?
You can put this solution on YOUR website!
a= b* sin A/sin B

Question 815953: What is the smallest possible integer perimeter of a triangle which has sides 5 and 10?
You can put this solution on YOUR website!
The third side must be larger than 10-5 = 5 units.

Let x be the third unknown side. So if the third side must be larger than 5 units, then we can say x > 5.

The perimeter of the triangle is

P = s1 + s2 + s3

P = 5+10+x

P = 15+x

Now if x > 5, then this means that 15+x > 20 (add 15 to both sides of the original inequality)

So the perimeter must be larger than 20 units. If the perimeter is an integer (or whole number), then the smallest it can be is 21 units.

Question 815885: The supplement of an angle is three times as large as the complement of the same angle. What is the measure of the complement?
You can put this solution on YOUR website!
```
Hi,
The supplement of an angle 'x' is three times as large as the complement of the same angle.
Question states***
180°-x = 3(90°-x)
2x =270° - 180° = 90°
x = 45°, its compliment is (90° - 45°) = 45°
135° = 3(45°)
```

Question 815811: how do you find x using 3 angles given?
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how do you find x using 3 angles given?
---------
What does x represent?

Question 815718: two forces, one of 10N and the other of 6N, act on a body. the direction of the forces are not known. a) what is the minimum magnitude of the resultant of these force? b) what is the maximum magnitude?
You can put this solution on YOUR website!
---
minimum magnitude of the resultant force:
the forces act at 180 degrees to each other:
absolute-value( 10N - 6N ) = 4N
---
maximum magnitude of the resultant force:
the forces act at 0 degrees to each other:
absolute-value( 10N + 6N ) = 16N
---
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---
---
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Question 815712: Two angles of an isosceles triangle are x and (x+10).find two possible value of x.
You can put this solution on YOUR website!
case 1:
x + x + (x+10) = 180
3x + 10 = 180
3x = 170
x = 56.666666 degrees
---
case 2:
x + (x+10) + (x+10) = 180
3x + 20 = 180
3x = 160
x = 53.333333 degrees
---
Solve and graph linear equations:
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---
---
Convert fractions, decimals, and percents:
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Question 815714: the hypotenuse of a right triangle is 28cm long and the length of one of the legs is 23cm, find the length of the other leg

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use pythagorean thm:
h = sqrt( aa + bb )
28 = sqrt( 23^2 + b^2 )
28^2 = 23^2 + b^2
784 = 529 + b^2
b^2 = 784 - 529
b^2 = 255
---
b = 15.97 cm
---
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---
---
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Question 815608: what is the greatest and smallest possible integral lengths of the hypotenuse of the right triangle if the two sides measures 8 cm and 5 cm?

You can put this solution on YOUR website!
use pythagorean thm:
h = sqrt( aa + bb )
---
h = sqrt( 8*8 + 5*5 )
h = sqrt( 64 + 25 )
h = sqrt( 89 )
h = 9.434
---
this is a trick question.
this triangle cannot have a hypotenuse with an integral length (i.e. a hypotenuse whose length is an integer value).
---
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---
---
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Question 815602: If a 650-cm ladder is placed against a building at a certain angle, it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm higher up, how much closer will the ladder be to the building?
You can put this solution on YOUR website!
use pythagorean thm:
h = sqrt( aa + bb )
---
position 1:
L = h = 650 cm
a = 520 cm
650 = sqrt( 520*520 + bb )
650*650 = 520*520 + bb
bb = 650*650 - 520*520
b = 390 cm
---
position 2:
L = h = 650 cm
a = 520 + 80 = 600 cm
650 = sqrt( 600*600 + bb )
650*650 = 600*600 + bb
bb = 650*650 - 600*600
b = 250 cm
---
the ladder will be closer to the building by:
390 - 250 = 140 cm
---
Solve and graph linear equations:
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---
---
Convert fractions, decimals, and percents:
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Question 815507: How do you find the perimeter of a triangle when one of the side lengths is missing?
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How do you find the perimeter of a triangle when one of the side lengths is missing?
-----------
It's not possible without additional info.

Question 815424: The length of the median to the hypotenuse of an isosceles, right triangle is 10 units. What is the length of a leg of the triangle, in units? Express your answer in simplest radical form.
You can put this solution on YOUR website!
the median to the hypotenuse forms a new isosceles right triangle with each leg of the original triangle, so each leg length (L) is given by:
---
L = sqrt( m^2 + m^2 )
where m is the length of the median
---
L = sqrt( 10^2 + 10^2 )
L = sqrt( 2*100 )
---
L = sqrt(2)*10
---
Solve and graph linear equations:
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---
---
Convert fractions, decimals, and percents:
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Question 815290: Prove that the triangle with vertices A(-4,2), B(1,6),C(1,-2) is isosceles (find the measures of the base angle)
You can put this solution on YOUR website!
```
Hi,
AB =  = AC =
Angle C   sin θ =

```

Question 815281: What is the area of a triangle when the base is 2 1/2 and the Height is 5/8?
You can put this solution on YOUR website!
A=(5/2*5/8)/2=
(25/16)/2=
25/16*1/2=25/32 sq units

Question 814964: There is an isosceles triangle with 2 equal sides measuring 15m. Find the vertex angle if the area is 112.5 square meters.
I've tried to solve this formula using various equations but I can't seem to get it..

Answer by Edwin McCravy(9716)   (Show Source):
You can put this solution on YOUR website!
```If you can remember your perfect squares you'll
remember that 15² is 225 and that is exactly twice
the area of 112.5m².  So a square which is 15m on a
side has exactly twice that area.

Therefore since the triangle is isosceles it can
only be half of a 15m×15m square cut across the
diagonal.  So its vertex angle is the interior
angle of a square and therefore is 90°.

If that's too much for you, then you can work it
out this way. Draw ΔABC

Draw the line CE, which is the median, vertex angle bisector and
altitude from the vertex to the base (in green).  Label it h
and label each of the equal halves of the base AE=BE=x.

Area = base·height

The base is 2x, so

121.5 = (2x)(h)

121.5 = xh

And by the Pythagorean theorem,

x²+h² = 15²
x²+h² = 225

So you have this system to solve

x²+h² = 225
121.5 = xh

Remove the decimal by multiplying
the second equation by 2

225 = 2xh

2xh = 225

Make a perfect square trinomial by subtracting
that equation from both sides of

x²+h² = 225

to make it a perfect square trinomial:

x²-2xh+h² = 0

(x-h)(x-h) = 0

(x-h)² = 0

x-h=0

x=h

That tells us that congruent right triangles
ΔACE and ΔBCE are isosceles and the base
angles of an isosceles right triangle
are 45° each, so
∠ACE = ∠BCE = 45° and

∠ACB = ∠ACE+∠BCE = 45°+45° = 90°

Edwin```

Question 815046: In a triangle, one angle measures 46° while another measures of 37°. What is the measure of the remaining angle?
You can put this solution on YOUR website!
In a triangle, one angle measures 46° while another measures of 37°. What is the measure of the remaining angle?
----------
The sum of the 3 angles is 180 degs

Question 815052: two sides of a triangle have lengths of 8 m and 5 m the included angle measures 53 degrees whats the area of the triangle
You can put this solution on YOUR website!

You want height to find area.
Take one of the given sides as a base. Use the 8 m as a base.
. If you try , this would give just the projection of the 5 meter side onto the base, which is nice, but not what you want.

AREA will be

Question 815027: starting from point A, a boat sails due south 5 miles, then due east 4 miles, then due south again 6 miles, how far is the boat from point A?
You can put this solution on YOUR website!
total of 5+6-11 south and 4 east
11^2+4^2-c^2
c = 11.705

Question 814987: I have a triangle. The right side and the left side have a line showing they are congruent. The left hand corner of the triangle is 35 degrees. The right hand corner is x. And the top is y.
So it is a triangle with 3 spots. 2 in the corner, one on the top. The left corner is 35 degrees and the other two spots are x and y. Can you find the value of x and y.

You can put this solution on YOUR website!

In a triangle, when left side and right side are congruent, then, that triangle is a isosceles triangle. So, as per the properties, the angles opposite to the congruent sides are also congruent. So, x = 35 degrees as left corner = 35 degrees.
The sum of the angles of a triangle = 180 degrees.
So, the bottom angles + top angle = 180 degrees.
i.e. 35 + 35 + y = 180 degrees. i.e. 70 + Y = 180 degrees.
Therefore, y = 180-70 degrees. i.e. y = 110 degrees.
I hope it is clear to you. All the best. Feel free to contact me at gsmani9@yahoo.com.

Question 815025: in a right triangle, if one side is 8 and the other side is 17 what is the missing length
You can put this solution on YOUR website!
one side = 8 units

hypotenuse = 17 units

So, other side = 15 units.
If we take the other side = 17 units, then
Hypotenuse = which would fetch 18.78829 units.

All the best !
gsmani Iyer

Question 815029: find the center and the radius of a circle with the equation
(6-x)^2+(y+5)^2=37

You can put this solution on YOUR website!
```
Hi,
find the center and the radius of a circle with the equation
(6-x)^2+(y+5)^2=37
Standard Form of an Equation of a Circle is
where Pt(h,k) is the center and r is the radius
(6-x) = -(x-6)  and [-(x-6)]^2 = (x-6)^2
(x-6)^2+(y+5)^2=37
C(6,-5)  ,     r =

```

Question 814999: What is the altitude of an equilateral triangle whose perimeter is 6 to the square root of 6
You can put this solution on YOUR website!
Difficult to draw within the system, but I'll describe it:

Draw a triangle, equilateral; form altitude and call this length h. Label each side of the equilateral triangle as x. The altitude reaching the bottom or base side intersects this side to form two lengths x/2. Also, the altitude, h, cuts the triangle into two congruent 30-60-90 triangles. You can use pythagorean theorem for ONE of these triangles ( or the other as well).

You have and because of the given information about perimeter, .

That is enough developed information. Can you solve for h?

-------------------------------
After just solving for h myself, I wonder, why do you want the answer to the nearest square root of 6 and not to nearest square root of 3 ?
..
..
In other words, why do you want ?

Question 814989: I have a triangle. The right side and the left side have a line showing they are congruent. The left hand corner of the triangle is 35 degrees. The right hand corner is x. And the top is y.

So it is a triangle with 3 spots. 2 in the corner, one on the top. The left corner is 35 degrees and the other two spots are x and y. Can you find the value of x and y.

You can put this solution on YOUR website!

If two sides are congruent then the angles opposite the two congruent sides must be congruent (isosceles triangle). So x = 35. You can calculate y because the sum of the measures of the angles of a triangle is always 180 degrees and since you now know two of the three angles...

John

My calculator said it, I believe it, that settles it

Question 814752: The sides of an isosceles triangle are 27, 27, and 12yd long. What is the area of the triangle?
Do not round any intermediate computations, and round your answer to the nearest tenth. i need help on how to solve this step by step

You can put this solution on YOUR website!
The sides of an isosceles triangle are 27, 27, and 12yd long.
What is the area of the triangle?
:
We need to find the height of the triangle to find the area
:
Draw the triangle, with the base as 12 yd, draw the height, a perpendicular line from the center of the base, bisecting the top angle.
Note that you have two right triangles,
one leg is half the base, 6
one leg is the height h
one side is the hypotenuse, 27
Using pythag
6^2 + h^2 = 27^2
36 + h^2 = 729
h^2 = 729 - 36
h^2 = 693
h = is the height of the triangle
:
A = b*h
A = *
A = 157.949
A = 157.9 sq/yds

Question 814612: find the lengths of the sides of a triangle are in the ratio 17:10:9. find the lengths of the three sides if the area of the triangle is 576msquared
You can put this solution on YOUR website!
Heron's Formula for area is
A = sqrt(s(s-a)(s-b)(s-c) where s = (a + b + c)/2 with a,b,c being side lengths.
Since the side ratios are 17:10:9 we can write
rs = r(17+10+9)/2 = r*(36)/2 = r*18 = 18r where r is proportion factor
A =
A =
A =
Factoring the numbers we get
A =
A =
A =
A =
A =
Since A = 576, and solving for r
576 =
Divide each side by 36
16 =
So r = 4
This means that our side lengths are 4*17 , 4*10 , 4*9
The side lengths of our triangle are 68 , 40 , 36