Question

Katherine wants to construct a small box with a volume of 20 cubic inches with the following specifications. The length of a box is five more than its width. Its depth is one less than its width. What are the dimensions of the box in simplest radical form and rounded to the nearest hundredth? Only and algebraic solution will receive full credit.

Answer 1

In this question, you have to form the equation given the formula of the volume : L x W x D
L = W+5
W = W
D = W-1

(W+5)(W)(W-1) = 20
(W^2+5W)(W-1) = 20
W^3+4W^2-5W-20 = 0

Get the roots by factoring it out.
(w +4) *(w +2.236) *(w -2.236)

So the roots are: -4, -2.236, 2.236.
Since we're talking about dimensions, let's use the positive root..

L = 7.24
W = 2.24
D = 1.24