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 455 ft3 (cubed). What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid.
Answer provided by our tutors
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 455 ft3 - this means the volume of the space V = 455 ft^3
V = l*w*h
plug h = w - 2 into the last equation
13*w*(w - 2) = 455
by solving we find and consider the positive roots
w = 7 ft
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h = w - 2
h = 7 - 2
h = 5 ft
the dimensions of the cargo space are 13 ft, 7 ft and 5 ft.