You construct an open box with a square base from 128 square inches of material. The height of the box is 2 inches. What are the dimensions of the box?

Answer 1

Answer 2

Since the length and width are the same, we have a base area of a² inches squared.

We also have 4 sides with an area of 2a inches squared each.

We don't have a top, but if we did, it would also have an area of a² inches squared.

a² + 8a = 128

a² + 8a - 128 = 0

(a + 16)(a - 8) = 0

a + 16 = 0

a = -16

Since we don't measure in negative numbers, we distegard this answer.

a - 8 = 0

a = 8

The dimensions of our box are 8 in x 8 in x 2 in.

Answer 3

Hi, Sabrina.

Okay, since it's a square box, then the length and width are the same.

Let's call the length, x.

The height of the box is 2 inches.

So, the area of the base of the box is x²

^{Then the area of the sides are each 2x}

^{and there are 4 sides, so the total surface area of the box is:}

x² + 4(2x) (The area of the base and 4 sides)

x² + 4(2x) = 128

x² + 8x = 128

x² + 8x - 128 = 0

(x - 8)(x+16) = 0

Since the length of the box is a positive number, x must equal 8.

So, therefore the dimensions of the box are:

8 in x 8 in x 2 in