Find the length of the shorter leg of a right triangle if the longer leg is 5 feet more the the shorter leg and hypotenuse is 5 feet less than twice the shorter leg

Answer 1

L=5+S

H= 2S -5

H^2 + S^2 + L^2 = S^2 + 25 +10S + S^2 = 2S^2 + 10S + 25

4s^2 -20S + 25 = 2S^2 + 10S +25

2S^2 -30S = 0

S^2 -15S = 0

S(S-15) = 0

S = 15 feet = shortest side

L= 15 + 5 = 20 feet

H= 30-5 = 25 feet

15-20-25 is a 5 factor multiple of a common 3-4-5 right triangle. 9+16 = 25