Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which se cuts out 6-in. squares from each corner. The length of the original piece of cardboard is 12 in. more than the width. If the volume of the box is 1728 in^3, determine the demenisons of the original piece of cardboard.

Question
Asked Sep 7, 2019

Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which se cuts out 6-in. squares from each corner. The length of the original piece of cardboard is 12 in. more than the width. If the volume of the box is 1728 in^3, determine the demenisons of the original piece of cardboard. 

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Step 1

Let the width of rectangular sheet is x inches  and then its width is (x+12)inches. After cutting of 6 inches squares from each corner, we get box of length x inches , width (x-12) inches and height  6 inches.

l=(x+12)-12=x
w x12
h 6
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l=(x+12)-12=x w x12 h 6

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Step 2

After we , use the formula for volume of cuboid to get the quadratic in x.

V lwh
lwh 1728
x(x-12)(6) 1728
x(x-12)288
x212x 288=0
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V lwh lwh 1728 x(x-12)(6) 1728 x(x-12)288 x212x 288=0

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Step 3

Then , we solve the quadrtic for x. one of values of x is negative , which is not p...

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Math

Algebra

Equations and In-equations