# Questions on Word Problems: Geometry answered by real tutors!

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 Word Problems: Geometry Solvers Lessons Answers archive Quiz In Depth

Question 759317: A rectangle carpet has perimeter of 234 in. Length is 71 in more than the width what are the dementions of the carpet
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Perimeter = 2 x length + 2 x width
Width = x
Length = x + 71
234 = 2*(x + 71) + 2*(x)
234 = 2x + 142 + 2x
234 = 4x + 142
4x = 234 - 142
4x = 92
x = 23
Width = 23 inches
Length = 94 inches
Hope this helps.
:-)

Question 758909: Sheila made a scale drawing of a room. The actual room has a width of 16 feet and a length of 24 feet. Her drawing has a length of 3 inches. What is the width, in inches, of the scale drawing of the room?
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length 24 ft : 3 inches
288 inches:3 inches
96:1
Width 16 ft
192 inches
192/96 = 2 inches
Hope this helps.
:-)

Question 759147: a string 55 in. long is cut into 3 segmants. the first is twice as long as the second and the third is 5 inches less than the second
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x = Second piece
2x = First piece
x - 5 = Third piece
x + (2x) + (x - 5) = 55
4x - 5 = 55
4x = 55 + 5
4x = 60
x = 15.
First piece = 2x = 30 inches
Second piece = x = 15 inches
Third piece = x - 5 = 10 inches
total = 55 inches
Hope this helps.
:-)

Question 759247: find the area of a sector of a circle, given the radius is 46mm and whose central angle is 120 degrees. use pi 3.14
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Angle/360 = area of sector/Pi r^2
120/360 = area of sector/Pi * 46^2
Cross multiply
Area of sector = 120 * 3.14* 46^2/ 360
Area of sector = 2214.8 mm^2
Hope this helps.
:-)

Question 759023: One-fifth the perimeter of a building is 50 feet. The length of the building is 30 feet longer than the width. What is the area of the building?
You can put this solution on YOUR website!

the perimeter of a building is .
....eq.1......the perimeter of a building
of the perimeter is ; so, the perimeter of a building is =>
then

...solve for
......eq. 1a
if the length of the building is longer than the width , than
.......plug in eq.1a
......eq. 1a....solve for

now find

the area of the building is

Question 759001: A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft long. The triangle shown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft tall, how tall is the tree?

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with similar triangles the ratios of the corresponding sided will be equal. thus if the boys shadow is 2.5ft an dthe trees shadow is 10ft then the ratio is
2.5/10 which is 1/4
we know the boy is 5ft, so the tree will need to be 4 times as large, and thus is 20ft.

Question 759007: A rectangular room that is 1 foot longer than it is wide has an area of 90 square feet. How many feet long is the room?
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A rectangular room that is 1 foot longer than it is wide has an area of 90 square feet. How many feet long is the room?
-----------------
Find a pair of factors of 90 that differ by 1.

Question 758877: a rectangle has an area of 27 square inches.The length is one third as long as the width. Find the length and width of the recrtangle.
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a rectangle has an area of 27 square inches.The length is one third as long as the width. Find the length and width of the recrtangle
-----------
3 by 9

Question 758841: the sum of a number and 2 is 6 less than twice that number.
i have no idea how to put that into an equation.

You can put this solution on YOUR website!
n = a number

, the sum of the number and 2
, six less than twice the number

What does, IS, mean?

Question 758742: Find the cost of framing a rectangular picture with dimensions of 4 inches by 6 inches if framing material costs \$0.65 per inch
You can put this solution on YOUR website!
Total cost is perimeter times price per inch
c = 2(l+w)*0.65
c=1.3(6+4)
cost: \$13.00

Question 758568: in baseball a strike zone is normally a 17 in by 40 in rectangle. by what percent is the area increased by adding a 1.5 in border to the outside of the strike zone?
Found 2 solutions by josmiceli, Alan3354:
You can put this solution on YOUR website!
The dimensions will become
by or
by
in2
The original area was:

in2
The area is increased by 180 in2

You can put this solution on YOUR website!
in baseball a strike zone is normally a 17 in by 40 in rectangle. by what percent is the area increased by adding a 1.5 in border to the outside of the strike zone?
-----------------
17*40 = 680 sq inches
------
If 1.5" is add to each side, --> 20*40 = 800 sq inches
----
(800 - 680)/680 = 14/68
14*100/68 =~ 20.59% increase
==============
If it's added to the 40 inches also, you'll have to clarifiy that or calculate it as above.

Question 757670: The fence around my rectangular backyard is 46 feet long. My yard is 2 feet longer than twice the width. What is the width of my yard? What is the length?
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Width = x
Length = 2 + 2x
Perimeter = 2 x length + 2 x width
46 = 2 x (2 + 2x) + 2(x)
46 = 4 + 4x + 2x
46 = 4 + 6x
46 - 4 = 6x
42 = 6x
7 = x
Width = 7ft
Length = 16ft
Hope this helps.
:-)

Question 758429: would you be able to expalain to me this problem
the dimensions of a 8 cm x 8 cm square are increased by a scale factor of 5. Determine the area?

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the dimensions are 8 * 8.
the area is 8^ = 64
if you multiply the dimnensions by 5, then the area will be increased by a factor of 5^2 = 25.
example:
8 * 8 are the original measurements.
mulitply each dimension by a factor of 5 to get:
40 * 40 are the revised measurements.
the revised area is equal to 40 * 40 = 1600 which is equal to 25 * 64.
if the original dimnensions are x * x, then the revised measurements would be equal to (5x) * (5x) which is equal to 5*x*5*x which is equal to 5*5*x*x which is equal to 25*x^2.

Question 758127: twice the first angle is 20 deg less than the third, 1/2 of the third is 60 deg less than the sum of the 1st and 2nd angles.find the angles
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Three angles, A,B,C;
Just write an equation for what it says.
:
twice the first angle is 20 deg less than the third,
2A = C-20
or
C = 2A+20
:
1/2 of the third is 60 deg less than the sum of the 1st and 2nd angles.
.5C = A + B - 60
multiply both sides by 2
C = 2A + 2B - 120
therefore
2A+20 = A + B - 60
2A - A = B - 60 - 20
A = B-80
or
B = A+80
:
And assuming this is a triangle
A + B + C = 180
replace B with (A+80); replace C with (2A+20)
A + A+80) + 2a+20 = 180
4A + 100 = 180
4A = 180 - 100
4A = 80
Divide both sides by 4
A = 20 degrees
then
B = 20 + 80
B = 100 degrees
and
C = 2(20)+20
C = 60 degrees
:
20 + 100 + 60 = 180; confirms our solutions

Question 758158: A rectangular field is 90 meters wide and 120 meters long. A pathway is drawn diagonally from one corner to another. How long is the pathway
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Pythagorean question.
Consider a right angled triangle:
Upright side = 120 metres
Base side = 90 metres
The diagonal path is the hypotenuse
120^2 + 90^2 = hypotenuse^2
14400 + 8100 = hypotenuse^2
Hypotenuse^2 = 22500
Hypotenuse = square root of 22500
Hypotenuse = 150 metres
This is the length of the pathway.
Hope this helps.
:-)

Question 758236: A rectangle field is 40 feet wide and is enclosed by 220 feet of fencing. What is the area of the field in square feet?
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A rectangle field is 40 feet wide and is enclosed by 220 feet of fencing. What is the area of the field in square feet?
.
Let x = length of field
then
2(x+40) = 220
x+40 = 110
x = 70 feet length
.
area:
width*length
40*70 = 2800 square feet

Question 758196: how high is a tree that casts a 33 ft shadow at the same time a 5 ft pole casts a shadow which is 12 ft long?
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how high is a tree that casts a 33 ft shadow at the same time a 5 ft pole casts a shadow which is 12 ft long?
let x=height of the tree
x/33=5/12
x=5*33/12
x=13.75
height of the tree=13.75 ft

Question 758212: if the sum of the 1st term of a G.P is 38 and the 4th term exceeds the first term by 19, find the value of the first term and of the common ratio
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if the sum of the 1st term of a G.P is 38 and the 4th term exceeds the first term by 19, find the value of the first term and of the common ratio
------
What do you mean by "the sum of the 1st term is 38"?
=========
Cheers,
Stan H.
===============

Question 758137: 1. A local farm owner has just acquired another smaller farm with three silos for cattle feed. The shapes of the silos are right circular cylinders. Suppose one silo is 40 ft tall with a twelve foot diameter; another silo is 50ft tall with a 14ft diameter; and the third silo is 60ft tall with an 18ft diameter.
a. What is the combined capacity in cubic feet of al three silos?
b. If 1 quart of paint covers 100 sq feet, how many quarts of paint will the farmer need to paint the three silos and restore an appearance of newness?

You can put this solution on YOUR website!
Volume of a right circular cylinder
= Pi r^2 h
Ist Silo = Pi *6^2 * 40 = 4523.89 cuft
2nd Silo = Pi * 7^2 * 50 = 7696.90 cuft
3rd Silo = Pi * 9^2 * 60 = 15268.14 cuft
Total Volume = 27488.93 cuft.
Surface Area of a right circular cylinder
= Pi r^2 + 2 Pi r h (Assuming only the top
of the silo needs painting.)
1st Silo= Pi * 6^2 + 2*Pi*6*40 = 1621.06 ft^2
2nd Silo = Pi * 7^2 + 2+Pi*7*50 = 2353.05 ft^2
3rd Silo = Pi * 9^2 + 2 * Pi * 9 * 60 = 3647.39 ft^2
Total Surface Area = 7621.5 ft^2
Divided by 100 sq ft = 76 215
Requiring 77 quarts of paint.

Question 757984: A rain gutter is made from sheets of aluminum that are
12 inches wide by turning up the edges to form right angles.
Determine the depth of the gutter that will maximize its
cross-sectional area and allow the greatest amount of water to flow.
What is the maximum cross-sectional area?

You can put this solution on YOUR website!
A rain gutter is made from sheets of aluminum that are
12 inches wide by turning up the edges to form right angles.
Determine the depth of the gutter that will maximize its
cross-sectional area and allow the greatest amount of water to flow.
--------------------
Let the height be "x"
Then base is 12-2x
------------
Area = x(12-2x) = -2x^2 + 12x
----
Maximum of this parabola occurs when x = -b/(2a) = -12/(-4) = 3
That is the depth of gutter.
------
That cross-section area is x(12-x) = 3*9 = 27 sq in.
========================================
Cheers,
Stan H.
=======================

Question 757867: which of the following sets of numbers could be the lengths of the sides of the triangles?
A. 32mm, 14mm, 22mm
B. 32mm, 14mm, 18mm
C. 32mm, 14mm 46mm
D. 32mm, 14mm 14mm

You can put this solution on YOUR website!
which of the following sets of numbers could be the lengths of the sides of the triangles?
-----
Rule:
each side is < (sum of other 2 sides)
each side is > (difference of the other 2 sides)
A. 32mm, 14mm, 22mm
OK
---------------------------
B. 32mm, 14mm, 18mm
No because 32 is not less than 14+18
-----------------------------
C. 32mm, 14mm 46mm
No because 46 is not less than 32+14
-------------------------------
D. 32mm, 14mm 14mm
No because 32 is is not less than 14 + 14
===================
Cheers,
Stan H.
===================

Question 757835: two garden plots are to have the same area. one is square and one is rectangular. the rectangular plot is 2 meters wide and 32 meters long.

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Area of the rectangle = L*W = 32*2 = 64m sq
A square has equal sides so sqrt64 = 8m per side.

Question 757571: The legs of an isosceles right triangle each measure 10 inches .what is the length of the hypotenuse of this triangle , to the nearest tenth of an inch ?
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10^2 + 10^2 = Hypotenuse^2
200 = Hypotenuse^2
Hypotenuse = sqrt 200
Hypotenuse = 14.1 inches.
Hope this helps.
:-)

Question 757456: At a certain time of day, a tree that is x feet tall casts a shadow that is x-17 meters long. If the distance from the top of the tree to the end of the shadow is x+8 meters, what is the height,x, of the tree?
You can put this solution on YOUR website!
A Pythagoras question.
Tree = x
Distance from top of tree
to end of shadow = x + 8
So x^2 + (x - 17)^2 = (x + 8)^2
x^2 +(x^2 - 34x + 289) = (x^2 + 16x + 64)
Combine and collect like terms.
x^2 - 50x + 225
(x - 5)(x - 45)
So either x = 5 or x = 45
As the shadow = (x - 17) I would
discount x = 5.
Tree height = 45ft
Distance from top of
= 53ft.
Hope this helps.
:-)

Question 757511: rectangle 15cm wide having perimeter of 64cm is cut into 2 right angled triangle along the diagonal what is the area of each triangle?
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Perimeter of a rectangle = 2 * length +
2 * width.
64 = 2x + 30
2x = 64 - 30
2x = 34
x = 17
Length = 17cms
Therefore Area = length * width
= 17cms * 15cms
= 255 cm^2
If the rectangle is divided into 2
Each triangle would have an area
of 255/2 = 127.5 cm^2
Hope this helps.
:-)

Question 754474: The sum of two integers is 246 and the larger number is 27 more than 2 times the smaller number. Find the two integers.
You can put this solution on YOUR website!

Substitution

Question 755946: the sum of all interior angles of a regular polygon is 1080 degree. what is the measure of each of its exterior angle?
You can put this solution on YOUR website!
Formula for sum of interior angles of a polygon is
n is the number of sides of the polygon
Formula for measure of single exterior angle of a regular polygon is where n is the number of sides of the polygon.
So to find the measure of the exterior angle we first need to find out how many sides the polygon has. To do that we use the interior sum formula and solve for n.

Now plugging n into our exterior angle formula we get

Question 757425: A woman foot is 7in long. If she steps off the length of a room by placing directly in front of the other,and finds room to be 10 steps. What is the length of the room in inches?
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The woman's foot is 7 inches. If she places one foot in front of the other 10 times then she will have covered 7 times 10 inches.
The length of the room is inches.

Question 757288: A tree 24 feet tall cast a shadow 12 feet long. Ronnie is 6 feet tall. How long is Ronnies shadow?
You can put this solution on YOUR website!
This is a similar triangle question.
You have to use the ratio of the two similar sides
24/6 = 12/x
Cross multiply
24x = 72
Divide both sides by 24
x = 3
Therefore Ronnie's shadow will be 3 feet long.
Hope this helps.
:-)

Question 757293: Amount of fencing in linear feet needed for the perimeter of a rectangular lot with diagonal length 38 meters and a side length 32 meters?
You can put this solution on YOUR website!
if the diagonal measured 38 metres and the side length
measured 32 metres, using Pytagoras the base side measures 20.5 metres
Base length^2 + side length^2= diagonal length^2
Diagonal length^2 - side length^2 = base length^2
Square root of base length square = 20.5 metres.
Perimeter = 2 x base length + 2 x side length.
= 2 x 32 + 2 x 20.5
= 64 + 41
= 105 metres = 344.49 feet
Hope this helps.
:-)

Question 757336: Now, suppose our Area needs to be 100 square feet. What values would the length need to be if our widths are 5 feet, 25 feet, 4 feet, and 50 feet?

You can put this solution on YOUR website!
If you require an area of 100 square feet.
Widths Lengths
5ft --- 20ft
25ft--- 4ft
4ft--- 25ft
50ft--- 2ft
Hope this helps.
:-)

Question 757278: what is the longest chord passing through the centre of a circle
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by definition, a is the longest chord passing through the center of the circle

Question 757169: three squares have sides with lengths a,b and c. if b is 20%greater than a, c is 25%greater than b, then by what percent is the area of the largest square greater than the area of the smallest square
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three squares have sides with lengths a,b and c.
if b is 20%greater than a, c is 25%greater than b,
so b=a+20%a=1.2a
& c=b+25%b=1.25b=1.25*1.2a=1.5a
so the sides of the 3 squares are a,1.2a & 1.5a
now it is clear that greatest square is of sides 1.5a & smallest is of a
so the areas are (1.5a)^2=2.25a^2 & a^2
the percent difference in the area of the largest square & the smallest square
=(2.25a^2-a^2)*100/a^2=(2.25-1)*100=125%

Question 756887: the volume of a pyramid is 108cm3 .the pyramid is 6ft tall.what is the area of the base of the pyramid?please show your work so I can understand.thanks
You can put this solution on YOUR website!
volume of the pyramid with height h & base area a is (1/3)*a*h=ah/3
so ah/3=108 & h=6
so a=108*3/6=54 ft sqrd

Question 756907: Seventeen spires grace the majestic Cadet Chapel at the Air Force Academy in Colorado Springs, CO. Each spire is an isosceles triangle with a 40° vertex angle. Find the measure of each base angle
You can put this solution on YOUR website!
Isosceles triangles have two equal
sides and two equal angles.
If the vertex angle is 40 degrees
then the base angles will be 180 -
40 = 140/2 = 70 degrees each.
Hope this helps.
:-)

Question 756663: What is the approximate area of a flower bed that is 12 feet in diameter? ( Round off your answer to the next higher square foot.)
You can put this solution on YOUR website!
What is the approximate area of a flower bed that is 12 feet in diameter? ( Round off your answer to the next higher square foot.)
-------------
r = 6 ft

Question 756496: A metal strip is being installed around a workbench that is 8 feet long and 3 feet wide. Find how much stripping is needed
You can put this solution on YOUR website!
The perimeter is the distance round an
object. The workbench is a rectangle, so
perimeter = 2 * length + 2 * width
= 2 * 8ft + 2 * 3ft
= 16ft + 6ft
= 22 feet of stripping required.
Hope this helps.
:-)

Question 756497: The length of a rectangle is 4 times its width. the area is 144 cm^2. Find the dimensions of the rectangle.
You can put this solution on YOUR website!
Width = x
Length = 4x
Area = Length * Width
144 = 4x (x)
144 = 4x^2
4x^2 = 144
x^2 = 36
x = square root of 36
x = 6
Therefore width = x = 6cm
length = 4x = 24cm
Area = w * w
= 6 * 24
= 144 cm^2
Hope this helps.
:-)

Question 756500: What is the approximate area of a flower bed that is 12 feet in diameter? (Round off your answer to the next higher square foot.)
You can put this solution on YOUR website!
What is the approximate area of a flower bed that is 12 feet in diameter? (Round off your answer to the next higher square foot.)
.
radius = diameter/2 = 12/2 = 6 feet
area = (pi)r^2
area = (3.14)6^2
area = (3.14)36
area = 113.04
round to next higher square foot:
area = 114 square feet

Question 756348: How many tons of dirt would this be?
210 feet long by 90 feet wide by 14 feet deep

You can put this solution on YOUR website!
The description is not complete but just know there would be a value D pounds per cubic feet for the "dirt". You have a volume description and if you have the density D, then you can find the "pounds" of this volume of dirt.

You would need to know the value of D if you want the value of pounds for this dirt.

Question 756351: I need help with the following word problem:
The total surface area of a right circular cylinder is 54π square inches. If the altitude of the cylinder is twice the length of a radius, find the altitude of the cylinder.

You can put this solution on YOUR website!
The total surface area of a right circular cylinder is 54π square inches. If the altitude of the cylinder is twice the length of a radius, find the altitude of the cylinder.
---
Equations:
h = 2r
(pi)r^2 = 54(pi)
---
r^2 = 54
---
r = 3sqrt(6) inches
---
h = 2r = 6sqrt(6) inches
============================
Cheers,
Stan H.
==============

Question 756165: Triangle ADE is proportional to Triangle ABC. The length of DE is 20 ft.; the length of AB is 6ft. and the length of BC is 8 ft. What is the length of AD ?

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From the two triangles ADE and ABC
Sides CB/ED = AB/ED
8/20 = 6/x
Cross multiply
8x = 120
x = 120/8
x = 15
Hope this helps.
:-)

Question 756127: the speed of sound is approximately 760 mph in air. if a gun is fired 5/7 miles away, how long will it take the sound to reach you?