SOLUTION: A rectangular piece of metal is 10cm longer than it is wide. Squares with sides of 2cm long are cut from the four corners of the piece of metal, and the flaps are folded upward to

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Question 541593: A rectangular piece of metal is 10cm longer than it is wide. Squares with sides of 2cm long are cut from the four corners of the piece of metal, and the flaps are folded upward to form an open box. If the volume of the box is 832cm cubed, what were the demensions of the original piece of metal? (V=LWH)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The dimensions of the box, in terms of W, the width would be:
V+=+L%2AW%2Ah Substitute: L = W+10, h = 2, and V = 832.
832+=+%28W%2B10-4%29%28W-4%29%2A2 Simplify.
832+=+2%28W%2B6%29%28W-4%29
832+=+2%28W%5E2%2B2W-24%29 Divide both sides by 2.
416+=+W%5E2%2B2W-24 Subtract 416 from both sides.
W%5E2%2B2W-440+=+0 Factor.
%28W-20%29%28W%2B22%29+=+0 Apply the "zero product rule".
W-20+=+0 or W%2B22+=+0 so...
W+=+20 or W+=+-22 Discard the negative solution as the width, W, is a positive quantity.
W+=+20cm. and...
L+=+W%2B10
L+=+30cm.