The longest side of the right triangle is 2 feet more than the middle side and the middle side is 1 foot less than twice the shortest side. Find the length of the shortest side.

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