The length of the longer leg of a right triangle is

13inches

more than three times the length of the shorter leg. The length of the hypotenuse is

14inches

more than three times the length of the shorter leg. Find the side lengths of the triangle.

A and b are legs

a^2+b^2=c^2

lets say

a>b

so

a=13+3b

c=14+3b

a^2+b^2=c^2

(13+3b) ^2+b^2 = (14+3b) ^2

9b^2+78b+169+b^2=9b^2+84b+196

10b^2+78b+169=9b^2+84b+196

minus 9b^2 both sides

b^2+78b+169=84b+196

minus 84b both sides

b^2-6b+169=196

minus 196 both sides

b^2-6b-27=0

factor

(b+3) (b-9) = 0

set to zero

b+3=0

b=-3, false, dimentions cannot be negative

b-9=0

b=9

shorter leg is 9

a=13+3b

a=13+3 (9)

a=13+27

a=40

c=14+3b

c=14+27

c=41

side legnths are

9in, 40in, 41in