A pizza box top with a square base is to be made from a rectangular sheet of cardboard by cutting six 1-inch squares from the corners and the middle sections and folding up the sides. If the area of the base is to 144 in^2, what piece of cardboard should be used.

Question

A pizza box top with a square base is to be made from a rectangular sheet of cardboard by cutting six 1-inch squares from the corners and the middle sections and folding up the sides.  If the area of the base is to 144 in^2, what piece of cardboard should be used.

Please explain the process, thanks in advance.

Reiny · Answer

the base must be x-2 by x-2 (x-2)^2 = 144 x-2 = ±√144 = ±12 , but obviously x must be positive x-2=12 so the base should be 14 by 14 make a sketch to verify.