Problema Solution
On moving day, Jorge needs to rent a truck. The length of the cargo space is 13 ft, and the height is 2 ft less than the width. The brochure indicates that the truck can hold 330 ft3 (cubed). What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid.
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Let
l = 13 ft the length of the cargo space
w = the width of the cargo space
h = the height of the cargo space
The height is 2 ft less than the width:
h = w - 2
The truck can hold 330 ft^3. This means the volume of the cargo space is V = 330 ft^3.
The volume of rectangular solid is:
V = l*w*h
Plug h = w - 2 and l = 13 into the last equation:
13*w*(w - 2) = 330
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w = 6.14 ft approximately
We need to ignore the negative solution since the width can only be positive.
h = w - 2 = 6.14 - 2 = 4.14 ft
The dimensions of the cargo space are 13 ft, 6.14 ft and 4.14 ft.