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