I have a piece of cardboard that is twice as long as it is wide. If I cut a 1-inch by 1-inch square from each corner and fold up the resulting flaps, I get a box with a volume of 144 cubic inches. What are the dimensions of the cardboard?
A)8 inches by 16 inches
B)14 inches by 28 inches
C)10 inches by 20 inches
D)12 inches by 24 inches
E)6 inches by 12 inches

Question

I have a piece of cardboard that is twice as long as it is wide. If I cut a 1-inch by 1-inch square from each corner and fold up the resulting flaps, I get a box with a volume of 144 cubic inches. What are the dimensions of the cardboard? 
A)8 inches by 16 inches 
B)14 inches by 28 inches 
C)10 inches by 20 inches 
D)12 inches by 24 inches 
E)6 inches by 12 inches

Quizplus · Accepted Answer

Let's assume the width of the cardboard is x inches, then its length will be 2x inches (as it is twice as long as it is wide).

When we cut out a 1 inch by 1 inch square from each corner and fold up the resulting flaps, the height of the box will be 1 inch. Thus, the dimensions of the box will be (x-2) inches by (2x-2) inches by 1 inch.

The volume of the box is given as 144 cubic inches. So, we have:

(x-2)(2x-2)(1) = 144

Simplifying this equation, we get:

2(x-2)(x-1) = 144

(x-2)(x-1) = 72

We can now easily see that x = 10 satisfies this equation. Therefore, the width of the cardboard is 10 inches and its length is twice that, which is 20 inches.

So, the dimensions of the cardboard are 10 inches by 20 inches, and the correct answer is choice C.

I Have a Piece of Cardboard That Is Twice as Long