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# The length of an open-top box is 4 cm longer than its width. The box was made from a 480-cm^2 rectangle sheet of material with 6 cm-by-6 cm

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The length of an open-top box is 4 cm longer than its width. The box was made from a 480-cm^2 rectangle sheet of material with 6 cm-by-6 cm squares cut from each corner. The height of the box is 6 cm. Find the dimensions of the box.

Guest Mar 28, 2015

#1
+80983
+10

Since four 6 x 6 squares were cut from the original, sheet, the new surface area is given by:

480 - 4(6 x 6) = 480 - 36(4)  = 480 - 144 = 336 cm^2

And the surface area of the box is given by

2[W + (W + 4)]6 = 336        where W is the width and W + 4 is the length...so we have

2[ 2W + 4]6  = 336

12[2W + 4]  = 336     divide both sides by 12

2W + 4  = 28      subtract 4 from both sides

2W  = 24           divide both sides by 2

W = 12cm    this is the width

W + 4   =  12 + 4  = 16cm      this is the length

CPhill  Mar 28, 2015
Sort:

#1
+80983
+10

Since four 6 x 6 squares were cut from the original, sheet, the new surface area is given by:

480 - 4(6 x 6) = 480 - 36(4)  = 480 - 144 = 336 cm^2

And the surface area of the box is given by

2[W + (W + 4)]6 = 336        where W is the width and W + 4 is the length...so we have

2[ 2W + 4]6  = 336

12[2W + 4]  = 336     divide both sides by 12

2W + 4  = 28      subtract 4 from both sides

2W  = 24           divide both sides by 2

W = 12cm    this is the width

W + 4   =  12 + 4  = 16cm      this is the length

CPhill  Mar 28, 2015

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