Question

Erdem is going to construct a rectangular paper box. He will make the box x inches wide. The length of the box will be 2 inches more than its width, and the height of the box will be 4 inches more than its width. Considering the possible values for the volume of the box, which answers are possible values of the box's width, x inches?

a) x = −11
b) x = −8
c) x = 14
d) x = 8
e) x = 5
f) x = −6

Answer 1

To find the possible values for the width x of the rectangular box Erdem is making, we consider only the positive measurements, as negative values are not plausible for physical objects. The possible values are c) x = 14, d) x = 8, and e) x = 5.

Step-by-step explanation:

Erdem is constructing a rectangular paper box with dimensions based on the width x. The length will be x + 2 inches and the height x + 4 inches. The volume of a rectangular box is found by multiplying its width, length, and height, so the volume formula in terms of x would be V = x(x + 2)(x + 4). For the box to physically exist and have a positive volume, the value of x must be positive. Also, as the dimensions are in inches, x must be a value that reflects a plausible size for a paper box. Analyzing the options given, we can eliminate any negative values immediately since a negative width does not make sense for a physical object.

Therefore, the possible values for the width x of the box are the positive values:

c) x = 14

d) x = 8

e) x = 5