SOLUTION: A rectangular sheet of brass is twice as long as it is wide. Squares, 3 cm times 3 cm, are cut from each corner , and the ends are turned up to form an open box having a volume of

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A rectangular sheet of brass is twice as long as it is wide. Squares, 3 cm times 3 cm, are cut from each corner , and the ends are turned up to form an open box having a volume of      Log On


   

Question 1056877: A rectangular sheet of brass is twice as long as it is wide. Squares, 3 cm times 3 cm, are cut from each corner , and the ends are turned up to form an open box having a volume of 1248cm^3. What are the dimensions of the original sheet of brass?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +L+ = the length in cm of the original sheet of brass
Let +W+ = the width in cm of the original sheet of brass
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After the squares are cut out from the corners,
The new length = +L+-+2%2A3+ cm
The new width = +W+-+2%2A3+ cm
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The volume, after the sides are turned up to make a box, is
+V+=+%28+L+-+6+%29%2A%28+W+-+6+%29%2A3+ ( note the height will be +3+ cm )
given:
+L+=+2W+
+V+=+1248+ cm^3
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+1248+=+%28+2W+-+6+%29%2A%28+W+-+6+%29%2A3+
+1248+=+%28+2W%5E2+-+6W+-+12W+%2B+36+%29%2A3+
+2w%5E2+-+18W+%2B+36+=+416+
+2W%5E2+-+18W+-+380+=+0+
+W%5E2+-+9W+-+190+=+0+
+%28+W+-+19+%29%2A%28+W+%2B+10+%29+ ( just by looking at it )
+W+=+19+ cm ( Can't use the negative value )
and
+L+=+2W+
+L+=+38+ cm
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The dimensions of the original sheet of brass are 19 x 38
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check answer:
+V+=+%28+L+-+6+%29%2A%28+W+-+6+%29%2A3+
+V+=+%28+38+-+6+%29%2A%28+19+-+6+%29%2A3+
+V+=+32%2A13%2A3+
+V+=+1248+ cm3
OK