SOLUTION: The hypotenuse of a right triangle measures 10 feet. The shorter leg measures 10 feet less than twice the length of the longer leg. How long is the shorter leg?

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Question 189631: The hypotenuse of a right triangle measures 10 feet. The shorter leg measures 10 feet less than twice the length of the longer leg. How long is the shorter leg?
Answer by jonvaliente(64) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of the longer leg
hypotenuse=10 feet
shorter leg = 2x-10
Pythagorean theorem:
10%5E2=x%5E2%2B%282x-10%29%5E2
100=x%5E2%2B%284x%5E2-40x%2B100%29
100=5x%5E2-40x%2B100
Subtracting 100 from both sides, we get:
0=5x%5E2-40x
Dividing both sides by 5x we get:
0=x-8
Adding 8 on both sides we get:
x=8
Shorter Leg = 2x-10 = 2*8-10=6 feet