Let x be the dimensions of the square base and y be the height of the square prism. The surface area of a square prism:
SA = 2•Base_Area + Lateral_Area = 2x2+4xy
We are interested in the lateral surface area or 4xy.
if x2=3x and y2 = 3y then
LA2 = 4(3x)(3y) = 4 • 9xy
Factor = LA2/LA = 4•9xy/4xy = 9