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.

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BleabyinfibiaG · Accepted Answer

From the figure, l=3x−5ft,w=2x−1ft, and h=2ft. The volume is 40ft3 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: 20=6x2−13x+5 Write in standard form: 0=6x2−13x−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=5ft.

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

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