The longer leg of a right triangle is 4cm longer than the shorter leg the hypotenuse is 8 cm longer than the shorter find the side lengths of the triangle

Let x  be  length of shorter leg

4cm longer than the shorter leg x +  4 = length of longer leg
 
hypotenuse is 8 cm longer than the shorter 
x + 8  = length of  hypotenuse

phytagorus rule 

x^2  + (x+4)^2 = (x+8)^2 

x^2 + x^2 +8 x + 4^2 = x^2 + 16x +  8^2

x^2 - 8x - 48 =0

(x + 4 ) (x - 12) - 0 

x= - 4    we reject negative number

so  x= 12