Question 228927
Let a=shorter leg, b=longer leg, c=hypotenuse
b=a+6
c=2a-6
a^2+b^2=c^2
a^2+(a+6)^2=(2a-6)^2
a^2+a^2+12a+36=4a^2-24a+36
2a^2+12a=4a^2-24a subtract 36 from each side.
a^2+6a=2a^2-12a divide each side by 2.
a^2-18a=0
a(a-18)=0 factor
a=0, a=18
18' shortest leg's length.
.
Ed