SOLUTION: A rectangular sheet of metal is 10 cm longer than it is wide. Squares, 5 cm on a side are cut from the corners of the sheet and the flaps are bent up to form an opentopped box havi

Question 198229: A rectangular sheet of metal is 10 cm longer than it is wide. Squares, 5 cm on a side are cut from the corners of the sheet and the flaps are bent up to form an opentopped box having volume 6 L. Find the original dimensions of the sheet of metal.(Recall that 1 L = 1000 cm^3)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let w represent the width. Then the length is w + 10. Since both the length and the width are reduced by 5 on each side, the width of the box becomes w - 10 and the length of the box is w + 10 - 10 or just w. The height of the box, given the 5cm cutouts, must be 5cm.

The volume of the box, in cubic centimeters, is

. And the volume of a rectangular solid is:

, so:

So, divide both sides by 5, distribute, put the equation into standard form, and solve the quadratic for

to obtain the original width. Remember to exclude the negative root because you are looking for a positive measure.

John

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