Question 277687
The hypotenuse of a right triangle is 6 more than the shorter leg. The longer leg is three more than the shorter leg. Find the length of the shorter leg.

Let the shorter leg be x

hypotenuse = x+6

Longer leg is x+3

(x+6)^2 = x^2+ (x+3)^2

x^2+12x+36 = x^2+x^2+6x+9

x^2-6x-27 =0

x^2-9x+3x-27=0

x(x-9)+3(x-9)

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

x=9 

the sides are 9, 12 15