Question

A packing company is doing an inventory of boxes. Their most popular box is display below. You can use the formula V = lwh to find the volume of the b

Solid Geometry
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asked 2021-05-07

A packing company is doing an inventory of boxes. Their most popular box is display below.
You can use the formula \(V = lwh\) to find the volume of the box.
The volume of the box is \(40 ft^{3}\). What is the value of x? Find the length and the width of the box. Describe any extraneous solutions.

Expert Answers (1)

2021-05-08

From the figure, \(l=3x−5 ft, w=2x−1 ft,\) and \(h=2 ft\). The volume is \(40 ft^3\) so we can write:
\(V=lwh\)
\(40=(3x−5)(2x−1)(2)\)
Divide both sides by 2:
\(20=(3x−5)(2x−1)\)
Expand the right side:
\(\displaystyle{20}={6}{x}^{{2}}−{13}{x}+{5}\)
Write in standard form:
\(\displaystyle{0}={6}{x}^{{2}}−{13}{x}−{15}\)
Factor the right side:
\(0=(6x+5)(x−3)\)
By zero-product property,
\(x=−56,3\)
Since \(x=−56\) gives negative length and width, then it is extraneous. Hence,
\(x=3\)
Using the value of \(xx\), the length is \(3(3)−5=4\) ft ft and the width is \(2(3)−1=5 ft.\)

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