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 189638: 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 jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Let us state the given:

Hypotenuse = c = 10 feet
Longer Leg = a = a
Shorter Leg = b = 2a-10

Going to our Pyth.Theorem:
c%5E2=a%5E2%2Bb%5E2
10%5E2=a%5E2%2B%282a-10%29%5E2
10%5E2=a%5E2%2B%282a-10%29%5E2
100=a%5E2%2B4a%5E2-40a%2B100
5a%5E2-40a%2Bcross%28100%29-cross%28100%29=0
5a%2Ahighlight%28%28a-8%29%29=0
a=8ft%29, Longer Leg

b=2a-10=2%2A8-10=16-10=red%286ft%29, Shorter Leg (answer)

Let's check:
c%5E2=a%5E2%2Bb%5E2
10%5E2=8%5E2%2B6%5E2
100=64%2B36
100ft=100ft
Thank you,
Jojo