A rectangular piece of cardboard, whose area is 323 square inches, is made into an open box by cutting a 2-inch square from each corner and turning up the sides. If the box is to have a volume of 390 cubic inches, what size cardboard should you start with?

Question

A rectangular piece of​ cardboard, whose area is 323 square​ inches, is made into an open box by cutting a 2​-inch square from each corner and turning up the sides. If the box is to have a volume of 390 cubic​ inches, what size cardboard should you start​ with?

oobleck · Answer

If the cardboard is x by y then we need xy = 323 (x-4)(y-4)(2) = 390 So a 17x19 sheet of cardboard does the trick or, 323 = only has factors of 17 and 19 and it is easy to check that 13*15*2 = 390

A rectangular piece of​ cardboard, whose area is 323 square​ inches, is made into an open box by cutting a 2​-inch square from each corner and turning up the sides. If the box is to have a volume of 390 cubic​ inches, what size cardboard should you start​ with?

A rectangular piece of cardboard, whose area is 323 square inches, is made into an open box by cutting a 2-inch square from each corner and turning up the sides. If the box is to have a volume of 390 cubic inches, what size cardboard should you start with?