SOLUTION: The length of the longer leg of a right triangle is 19 inches more than five times the length of the shorter leg. The length of the hypotenuse is 20 inches more than five times the

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Question 1148845: The length of the longer leg of a right triangle is 19 inches more than five times the length of the shorter leg. The length of the hypotenuse is 20 inches more than five times the length of the shorter leg. Find the side lengths of the triangle.
Answer by ankor@dixie-net.com(22740) (Show Source):
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a^2 + b^2 = c^2
b is the shorter leg
The length of the longer leg of a right triangle is 19 inches more than five times the length of the shorter leg.
a = 5b + 19
The length of the hypotenuse is 20 inches more than five times the length of the shorter leg.
c = 5b + 20
Find the side lengths of the triangle.
(5b+19)^2 + b^2 = (5b+20)^2
FOIL
25b^2 + 95b + 95b + 361 + b^2 = 25b^2 + 100b + 100b + 400
25b^2 + 190b + 361 + b^2 = 25b^2 + 200b + 400
combine on the left
25b^2 - 25b^2 + b^2 + 190b - 200b + 361 - 400 = 0
b^2 - 10b - 39 = 0
factors to
(b-13)(b+3) = 0
Positive solution is all we want here
b = 13
then
a = 5(13) + 19
a = 84
and
c = 5(13) + 20
c = 85
:
:
Check:
= 85