Question

On moving day, Guyton needs to rent a truck. The length of the cargo space is 10 ft, and the height is 2 ft less than the width. The brochure indicates that the truck can hold 480 cubic feet. What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid.

a) Width: 16 ft, Height: 14 ft, Length: 10 ft
b) Width: 12 ft, Height: 10 ft, Length: 10 ft
c) Width: 14 ft, Height: 12 ft, Length: 10 ft
d) Width: 15 ft, Height: 13 ft, Length: 10 ft

Answer 1

The dimensions of the cargo space based on the given volume and the relationship between the height and the width are not matching any of the provided options. The calculated width is 8 ft and the height is 6 ft with the given length of 10 ft for a volume of 480 cubic feet.

Step-by-step explanation:

The student has asked for help determining the dimensions of the cargo space in a moving truck that Guyton needs to rent. The cargo space is said to hold 480 cubic feet and its shape is that of a rectangular solid (rectangular prism). It is given that the length (L) of the truck is 10 ft, and the height (H) is 2 ft less than the width (W). The formula to calculate the volume (V) of a rectangular solid is V = L × W × H. Thus, with the volume known to be 480 cubic feet, and the length given as 10 ft, we can set up the equation 480 = 10 × W × (W - 2), since the height is two feet less than the width.

Solving the quadratic equation 10 × W × (W - 2) = 480 yields W(W - 2) = 48, or W² - 2W - 48 = 0. This factors to (W - 8)(W + 6) = 0. Since width cannot be negative, W = 8 ft. Therefore, height H = W - 2, which means H = 6 ft. The dimensions of the cargo space are: Width: 8 ft, Height: 6 ft, Length: 10 ft. This is not one of the options provided, so there might be a mistake in the question itself or the provided options.