Question 78134This question is from textbook Elementary Algebra
: Constructing a box. I have a piece of cardboard that is twice as long as it is wide. If I cut a 2-inch by 2-inch square from each corner and fold up the resulting flaps, I get a box with a volume of 32 cubic inches. What are the dimensions of the cardboard?
This question is from textbook Elementary Algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Constructing a box. I have a piece of cardboard that is twice as long as it is wide. If I cut a 2-inch by 2-inch square from each corner and fold up the resulting flaps, I get a box with a volume of 32 cubic inches. What are the dimensions of the cardboard?
:
Let x = the width
Then 2x = the length
:
If you draw this out, it will be apparent that the dimensions of the box are:
(x-4) by (2x-4) by 2
:
L * W * H = volume
:
(x-4)*(2x-4)* 2 = 32
:
2(2x^2 - 12x + 16) = 32
:
4x^2 - 24x + 32 - 32 = 0
:
4x^2 - 24x = 0
:
4x(x - 6) = 0
:
x = 0
and
x = +6 is the width, and 2(6) = 12 is the length
:
:
The dimension of the cardboard would be 6 by 12 by 2
:
Check the volume:
(6-4) * (12-4) * 2 =
2 * 8 * 2 = 32
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