Question

A box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of (x − 1) feet, and a height of (x + 9) feet. Find the dimensions of the box.

Answer 1

72 = l . w . h

72 = x . (x - 1) . (x + 9)

72 = (x² - x) . (x + 9)

72 = x³ + 9x² - x² - 9x

72 = x³ + 8x² - 9x

0 = x³ + 8x² - 9x - 72

0 = x² (x + 8) - 9 (x + 8)

0 = (x² - 9)(x + 8)

0 = (x - 3)(x + 3)(x + 8)

x = 3 or x = -3 or x = -8

so, x = 3

length = x = 3

width = x - 1 = 2

height = x + 9 = 12