A right triangle's longest side is the hypotenuse let x=longest, y=middle, and z=shortest x=y+2 y=2z-1 therefore x=(2z-1)+2=2z+1 find z z^2+y^2=x^2 by Pythagorean theorem plug in x and y in terms of z z^2+(2z-1)^2=(2z+1)^2 z^2+4z^2-4z+1=4z^2+4z+1 subtract the right-hand side's value from the left-hand side's z^2-8z=0 z(z-8)=0 z=0, 8 z cannot be zero as the sides must have some value to it. Therefore the shortest side is equal to 8
