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

he298c

he298c

Answered question

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 40ft3. What is the value of x? Find the length and the width of the box. Describe any extraneous solutions.

Answer & Explanation

BleabyinfibiaG

BleabyinfibiaG

Skilled2021-05-08Added 118 answers

From the figure, l=3x5ft,w=2x1ft, and h=2ft. The volume is 40ft3 so we can write:
V=lwh
40=(3x5)(2x1)(2)
Divide both sides by 2:
20=(3x5)(2x1)
Expand the right side:
20=6x213x+5
Write in standard form:
0=6x213x15
Factor the right side:
0=(6x+5)(x3)
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=5ft.

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