A rectangular box has a volume of 72x cubic inches. The width of the rectangular box is x inches, the length is 3x inches, and the height is (3x-1) inches. Find the dimensions of the rectangular box.

Answer 1

9x^3 -3x^2 = 72x

9x^2 -3x = 72

3x^2 -x = 24

3x^2-x -24 = 0

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

x-3=0

x = 3

3 by 9 by 8 = 216 cubic inches = 72(3)

dimensions are 3 inches by 9 inches by 8 inches

width = x = 3 inches

length = 3x = 9 inches

height = 3x-1 = 8 inches

volume = 72x = 216 in^3