SOLUTION: Thank you in advance. Need help, textbook show lousy examples to explain process needed to solve problem. This problem is confusing to me, The triangle appears to be scalene, ther

Algebra ->  Triangles -> SOLUTION: Thank you in advance. Need help, textbook show lousy examples to explain process needed to solve problem. This problem is confusing to me, The triangle appears to be scalene, ther      Log On


   

Question 509847: Thank you in advance. Need help, textbook show lousy examples to explain process needed to solve problem. This problem is confusing to me, The triangle appears to be scalene, there are no cong.sides of this triangle picture of the graph in the book.
The question is Triangle ABC has vertices A(0,8), B (6,0), C(15,0)
(B and C lie on the same line in the diagram, A is angled up toward the left then angles down to meet C)


USE THE DISTANCE FORMULA to find;
AB=
AC=
BC=
what is the perimeter of triangle ABC=_____
what is the area of triangle ABC=______square units.
Found 3 solutions by Alan3354, mananth, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
USE THE DISTANCE FORMULA to find;
AB=
AC=
BC=
what is the perimeter of triangle ABC=_____
what is the area of triangle ABC=______square units.
--------------------
AB+=+sqrt%286%5E2+%2B+8%5E2%29+=+10
AC+=+sqrt%2815%5E2+%2B+8%5E2%29+=+17
BC = 15-6 = 9
--------------
The perimeter is is the sum, 10+17+9
---------
The area = b*h/2 = 9*8/2 = 36 sq units

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The question is Triangle ABC has vertices A(0,8), B (6,0), C(15,0)
d(AB) =Distance between two points

d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
x1 y1 x2 y2
0 8 6 0
d= sqrt%28%280-8%29%5E2%09%2B%286-0%29%5E2%29
d= sqrt%28%28-8%29%5E2%09%2B%286%29%5E2%09%29
d= sqrt%28%28100%29++%09%29
dAB)= 10
d(BC)= Distance between two points
x1 y1 x2 y2
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
6 0 15 0
d= sqrt%28%28%09%090%09-%090%09%29%5E2%09%2B%09%28%0915%09-%096%09%29%5E2%09%29
d= sqrt%28%28%09%090%09%29%5E2%09%2B%09%28%099%09%29%5E2%09%29
d= sqrt%28%28%09%0981%09%29++%09%29
d(BC)= 9
d(CA)=Distance between two points
x1 y1 x2 y2
d= sqrt%28%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%29
15 0 0 8
d= sqrt%28%28%09%098%09-%090%09%29%5E2%09%2B%09%28%090%09-%0915%09%29%5E2%09%29
d= sqrt%28%28%09%098%09%29%5E2%09%2B%09%28%09-15%09%29%5E2%09%29
d= sqrt%28%28%09%09289%09%29++%09%29
d= 17
AB=10 , BC = 9, AC=17
Use Heron's formula to calculate the area
HERON”S FORMULA

Area of Triangle = sqrt%28s%2A%28s-a%29%28s-b%29%28s-c%29%29
where s = half the perimeter a,b,c are the sides of the triangle
A = 10 b= 9 c= 17

S= %28a%2Bb%2Bc%29%2F2 S= 18

Area =
Area =sqrt%28%0918%09%2A%09%28+%098%09%29%28%099%09%29%28%091%09%29%29

Area =sqrt%28%091296%09%29
Area = 36 sq. units
m.ananth@hotmail.ca




Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The distance formula:



where and are the coordinates of the given points.

You have three points, so you have three pairs of points. Use the distance formula 3 times to calculate the measure of the three sides. Add the three measures to calculate the perimeter.

The area is a little trickier. If you use segment BC as the base of the triangle, then the segment OA (Point O being the origin (0,0)) is the altitude of the triangle. Use the distance formula to calculate the measure of OA (or just do it by inspection of the graph) and then submit the base and altitude measures to the formula for the area of a triangle, namely the base times the altitude divided by 2.

This triangle has a very interesting property. The number of linear units in the perimeter is equal to the number of square units in the area.

John

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