By prepainga diagram, sides x, x+30 and x+60 form a right angle triange inside the rectangle. We can apply pythagoras theorem to this triangle and obtain the value of x. (x^2) + (x+30)^2 = (x+60)^2. By solving this equations and cancelling some terms we are left with a simple quadratic equation. Which is x^2 -60x -2700=0. This can be factorized be splitting the mid term and the value of x turns out to be 90. Hence shortest side =90.
