SOLUTION: please help. A rectangular piece of sheet metal has a length that is 4 in. less than twice the width. A square piece 2 in. on a side is cut from each corner. The sides are then

Algebra ->  Test -> SOLUTION: please help. A rectangular piece of sheet metal has a length that is 4 in. less than twice the width. A square piece 2 in. on a side is cut from each corner. The sides are then       Log On


   

Question 888812: please help.
A rectangular piece of sheet metal has a length that is 4 in. less than twice the width. A square piece 2 in. on a side is cut from each corner. The sides are then turned up to form an uncovered box of volume 256 in^3. Find the length and width of the original piece of metal.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Sheet metal, L=-4+2w using L for length and w for width.

Volume of the box is %28w-2%2A2%29%28L-2%2A2%29%2A2=256 or 2%28w-2%2A2%29%28L-2%2A2%29=256. Substitute for L and then solve for w.

2%28w-4%29%282w-4-4%29=256, some partial simplification start included;
%28w-4%29%282w-8%29=128
%28w-4%29%28w-4%29=64
No use in trying to multiply on the left because both members are square.
w-4=8
highlight%28w=12%29
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L=2w-4
L=24-4
highlight%28L=20%29