SOLUTION: The hypotenuse of a right triangle is 10. One side is 2 less than the other. Find the length of each leg.

Question 148671: The hypotenuse of a right triangle is 10. One side is 2 less than the other. Find the length of each leg.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a right triangle is 10. One side is 2 less than the other. Find the length of each leg.
:
Using our old friend: a^2 + b^2 = c^2
:
Let a = x
Let b = (x+2)
Given: c = 10
:
x^2 + (x+2)^2 = 10^2
FOIL (x+2)(x+2)
x^2 + (x^2 + 4x + 4) = 100
:
2x^2 + 4x + 4 - 100 = 0
:
2x^2 + 4x - 96 = 0
Simplify, /2
x^2 + 2x - 48 = 0
Factor
(x+8)(x-6) = 0
positive solution:
x = 6 is one leg and the other leg = 8
:
:
Check solution:
6^2 + 8^2 =
36 + 64 = 100 which is 10^2

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