SOLUTION: The longer leg of a right triangle measures two feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length

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Question 186887: The longer leg of a right triangle measures two feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length of all three sides.
Answer by uday1435(57) About Me  (Show Source):
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The longer leg of a right triangle measures two feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length of all three sides.
Let the shorter leg = s
Longer leg = 2s + 2
Hypotenuse = 2s+3
By Pythagorean theorem
(2s + 3)^2 = (2s+2)^2 + s^2
4s^2+12s + 9 = 4s^2 + 8s +4 + s^2
On simplification we get s^2 – 4s – 5 = 0
(s – 5) (s + 1) = 0
So s = 5, means The shorter leg = 5 feet , Longer leg = 2(5)+2 = 12 feet and the hypotenuse = 2(5) + 3 = 13 feet

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