A cuboid has sides such that the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units². Calculate the length of the shortest side.

The sides of the cuboid are as follows: x, x+1 and x+2. Total surface area of a cuboid is the area of each surface added together. Therefore 2x(x+2)+2x(x+1)+2(x+2)(x+1)= 52 units².

2x²+4x+2x²+2x+2x²+6x+4= 52

6x²+12x+4=52 

6x²+12x-48=0

x²+2x-8=0

Use Quadratic formula

x=2