SOLUTION: The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides

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Question 227543: The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the triangle
Answer by checkley77(12569) About Me  (Show Source):
You can put this solution on YOUR website!
c=3a-8
b=2a+8
a^2+b^2=c^2
a^2+(2a+8)^2=(3a-8)^2
a^2+4a^2+32a+64=9a^2-48a+64
5a^2-9a^2+32a+48a+64-64=0
-4a^2+80a=0
-4a(a-20)=0
a-20=0
a=20 ans.
b=2*20+8=40+8=48 ans.
c=3*20-8=60-8=52 ans.
Proof:
20^2+48^2=52^2
400+2,304=2,704
2,704=2,704