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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.

 Feb 15, 2020
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Let the shorter leg =S
The longer leg =5S + 19
Hypotenuse      =5S + 20
[5S + 20]^2 =[5S + 19]^2 + S^2, solve for S
S = 13 inches - the shorter leg
13 * 5 + 19 =84 inches - the longer side
13 *5 + 20  =85 inches - the hypotenuse
85^2 =84^2 + 13^2 - which balances. 

 
 Feb 15, 2020

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