The open box with a square base is to be constructed from 1056 square inches of material. The height of the box is 5 inches. Find the dimensions of the base.
A)34 inches by 34 inches
B)24 inches by 24 inches
C)44 inches by 44 inches
D)14 inches by 14 inches
E)39 inches by 39 inches

Question

Quizplus · Accepted Answer

Let the length of each side of the square base be x inches. The area of the base is then x^2 square inches. Since there are 4 sides to the base, the total material used for the base is 4x^2.

The height of the box is given as 5 inches. So, the total volume of the box is V = x^2 * 5 cubic inches.

From the given information, we have:

4x^2 + 2x(5) = 1056 (the material is used for the base and sides)
=> 4x^2 + 10x - 1056 = 0

We can factor this equation to get:

(2x + 33)(2x - 32) = 0

The positive solution for x is x = 16. This means that the dimensions of the base are 16 inches by 16 inches, and the correct answer is B.

The Open Box with a Square Base Is to Be