Question 128813
X^2+(X-6)^2=[2(X-6)-6]^2
X^2+X^2-12X+36=[2X-12-6]^2
2X^2-12X+36=(2X-18)^2
2X^2-12X+36=4X^2-72X+324
2X^2-4X^2-12X+72X+36-324=0
-2X^2+60X-288=0
-2(X^2-30X+144)=0
-2(X-6)(X-24)=0
X-24=0
X=24 ANSWER FOR THE LONGER LEG.
24-6=18 IS FOR THE SHORTER LEG
18^2+24^2=H^2
324+576=H^2
H^2=900
H=SQRT900
H=30 FOR THE HYPOTENUSE.