Question

Manufacturing a company is designing a new rectangular shipping box that must have a

volume of 24 cubic inches. The company has created a box with a width that is 2 inches less

than its length. The height is 5 inches greater than the length. What are the dimensions?

Answer 1

3in by 1in by 8in

Explanation:

Volume of the box = Length × Width × Height

Given

Volume = 24in³

If the width is 2inhes less than the length

W = L-2... 2

Also if the height is 5 inches greater than the length, then;

H = L+5 ... 3

Substitite 2 and 3 into the formula.

V= LBH

24 = L(L+5)(L-2)

24 = L(L²+3L-10)

24 = L³+3L²-10L

L³+3L²-10L-24 =0

Factorize

The factored form is

(L+2)(L²+L−12) = 0

L²+L-12 = 0

L²+4L-3L-12 = 0

L(L+4)-3(L+4) = 0

(L+4) = 0 and L-3 = 0

L = 3in

W = L-2

W = 3-2

L = 1in

H = L+5

H=3+5

H = 8in

Hence the dimension is 3in by 1in by 8in