8.2. Applications of the Pythagorean Theorem http://www.ck12.org
First, draw the altitude from the vertex between the congruent sides, which will bisect the base (Isosceles Triangle
Theorem). Then, find the length of the altitude using the Pythagorean Theorem.
72 +h^2 = 92
49 +h^2 = 81
h^2 = 32
h=√
32 = 4
√
2
Now, usehandbin the formula for the area of a triangle.
A=
1
2
bh=1
2
( 14 )
(
4
√
2
)
= 28
√
2 units^2Example B
Find the distance between (1, 5) and (5, 2).
MakeA( 1 , 5 )andB( 5 , 2 ). Plug into the distance formula.
d=√
( 1 − 5 )^2 +( 5 − 2 )^2
=
√
(− 4 )^2 +( 3 )^2
=
√
16 + 9 =
√
25 = 5
You might recall that the distance formula was presented asd=
√
(x 2 −x 1 )^2 +(y 2 −y 1 )^2 , with the first and second
points switched. It does not matter which point is first as long asxandyare both first in each parenthesis. In
Example 7, we could have switchedAandBand would still get the same answer.