Question 915198
short leg be x

The longer leg of a right triangle is 
3cm  longer than the shorter leg. (x+3)


The hypotenuse is 6cm  longer than the shorter leg. (x+6)


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

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

x^2-6x-27=0

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

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

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

x=9 

9,12, 15 cm are the lengths