Question

The length of a rectangular prism is three times as long as its width, and its height is two feet longer than its width. If the volume of the prism is 135 cubic feet, what is its width?

Answer 1

A rectangular prism is a polyhedron with six rectangular faces. To fully define a rectangular prism, one must know its length, width and height. The volume of a rectangular prism is expressed as the product of its dimensions - length, width and height. To calculate for its width, we use the volume formula.

V = l x w x h
From the given, we have:
l = 3w
h = 2 + w
V = 135 ft^3

Substituting the given expressions,
135 ft^3 = 3w (w) (2+w)
135 ft^3 = 6w^2 + 3w^3

Solving for w, we obtain the following values:
w1= 3
w2 = 2.5 + 2.96i
w3 = 2.5 - 22.96i

Since width should not have a negative value, the value of w should be 3 ft.