Question 1148845
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
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Check: 
 {{{sqrt(84^2 + 13^2)}}} = 85