SOLUTION: A rectangular piece of cardboard that is 3 feet longer than it is wide will be made into an open-topped box by cutting 2 ft squares out of each corner and folding up the sides. The
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-> SOLUTION: A rectangular piece of cardboard that is 3 feet longer than it is wide will be made into an open-topped box by cutting 2 ft squares out of each corner and folding up the sides. The
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Question 301672: A rectangular piece of cardboard that is 3 feet longer than it is wide will be made into an open-topped box by cutting 2 ft squares out of each corner and folding up the sides. The volume of the resulting box will be 140 cubic feet. Find the original dimensions of the cardboard. Can you help me with the formula to calculate this problem? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A rectangular piece of cardboard that is 3 feet longer than it is wide will be
made into an open-topped box by cutting 2 ft squares out of each corner and folding up the sides.
The volume of the resulting box will be 140 cubic feet.
Find the original dimensions of the cardboard.
:
Let x = the width of the piece of cardboard
then
(x+3) = the length of the cardboard
:
Cutting 2 ft squares out of each corner will give the box dimensions
(x+3-4) by (x-4) by 2 ft
which is:
(x-1) by (x-4) by 2
:
The volume
2*(x-1)*(x-4) = 140
FOIL
2*(x^2 - 4x - x + 4) = 140
2*(x^2 - 5x + 4) = 140
2x^2 - 10x + 8 - 140 = 0
2x^2 - 10x - 132 = 0
Simplify, divide by 2
x^2 - 5x - 66 = 0
Factors to
(x-11)(x+6) = 0
positive solution is what we want here
x = 11 ft is the width of the cardboard
then
11 + 3 = 14 ft is the length
:
:
Check solution by finding the vol of the box
(14-4)*(11-4)* 2 =
10 * 7 * 2 = 140
