Answer
6, 8, and 10
Work Step by Step
$x^2+(x+2)^2=(x+4)^2$
$x^2+x^2+4x+4=x^2+8x+16$
$2x^2+4x+4=x^2+8x+16$
$x^2-4x-12=0$
$(x-6)(x+2)=0$
$x-6=0$
$x=6$
$x+2=0$
$x=-2$ (we can't have a negative sidelength, so $x\ne-2$).
$x^2+(x+2)^2=(x+4)^2$
$6^2+(6+2)^2=(6+4)^2$
$36+8^2=10^2$
$36+64=100$
