Question

3. Bricks are delivered to a work site and stacked in rows and columns, forming a rectangular prism. The length of the prism is 1 foot greater than its width, and its height is 2 feet less than its width. Find the dimensions of the prism formed by the bricks, given that its volume is 40 cubic feet.

Answer 1

Volume of a rectangular prism = 40 cubic feet.

Volume of a rectangular prism = length * width * height

width = x
length = 1 foot greater than its width = x + 1
height = 2 feet less than its width = x - 2

l * w * h = 40 ft³
(x+1) * x * (x -2) = 40
(x² + x)(x-2)
x³ - 2x² + x² + 2x = 40
x³ - x² + 2x - 40 = 0

solve for the value of x. I used the calculator to get the volume.

width = x = 4
length = x + 1 = 4 + 1 = 5
height = x - 2 = 4 - 2 = 2

V = 4 * 5 * 2
V = 20 * 2
V = 40 ft³