SOLUTION: Eric is building an open top box using a piece of cardboard that is twice as long as it is wide. To make the walls of the box, he cuts a one inch square from each corner of the box
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Question 944103: Eric is building an open top box using a piece of cardboard that is twice as long as it is wide. To make the walls of the box, he cuts a one inch square from each corner of the box. If the volume of the box is 144 in2, what were the original dimensions of the cardboard?
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Eric is building an open top box using a piece of cardboard that is twice as long as it is wide. To make the walls of the box, he cuts a one inch square from each corner of the box. If the volume of the box is 144 in^3
what were the original dimensions of the cardboard?
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Original dimensions:: x and 2x
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New dimensions:: x-2 ; 2x-2 ; x
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Equations:
x(x-2)(2(x-1) = 144
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2x(x^2-3x+1) = 144
x^3 - 3x^2 + x - 72 = 0
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x = 5.34
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Cheers,
Stan H.
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Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Dimensions will be w and 2w, as variables.
Forming the open box, the volume is ;
You would next make of list of possible rational roots to check, and use synthetic division to find which root will work.
Instead of actually doing that, I am using the graphing feature of google.com to inspect the graph of the function for roots or zeros. (Replacement of w with x is necessary there.)
The root may be irrational, appearing to be extremely near to 5.24.
Maybe 5.24028...
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