Question

The volume of a rectangular prism is 165 cubic inches.

The length of the rectangular prism is 5 inches,

the width is x – 3, and the height is x + 5.

Find the value of x, and the dimensions of the rectangular prism.

Answer 1

Explanation:

volume = base area x height

base area = rectangle

so volume = l x w x h

5 x (x-3) x (x+5)

5 x (x^2 + 2x - 15)

5x^2 + 10x - 75 = 165

x^2 + 10x - 240

x = -8

x = 6

taking x = 6 because dimensions cannot be negative

length = 5 inches

width = 3 inches

height = 11 inches