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Question 1146199: Lorene plans to make a box from rectangular sheets of cardboard from which she cuts out 6 inches squares from each corner. The length of the original piece of cardboard is 12 inches more than the width. If the box is 1728 inches cubed, determine the dimensions of the original piece of cardboard.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Lorene plans to make a box from rectangular sheets of cardboard from which she cuts out 6 inches squares from each corner.
The length of the original piece of cardboard is 12 inches more than the width.
If the box is 1728 inches cubed, determine the dimensions of the original piece of cardboard.
:
let w = the original width of the rectangular sheet
the length is 12" more than the width, therefore:
(w+12) = the original length of the cardboard
:
Removing the 6" squares subtract 12" from the sheet dimensions
(w-12) * ((w+12)-12) = 1728
(w-12) * w = 1728
a quadratic equation
w^2 - 12w - 1728 = 0
U can use the quad formula, a=1; b=-12; c=-1728; but this Factors to
(w-48)(w+36) = 0
the positive solution
w = 48" is the width of the sheet
and
48 + 12 = 60" is length
:
:
Check
The box dimension, (corners subtracted) 48 * 36 = 1728
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