SOLUTION: Need help with the following: A box is being constructed by cutting 3-inch squares from the corners of a rectangualr sheet of metal that is 4 inches longer than it is wide. If t

Question 267524: Need help with the following:
A box is being constructed by cutting 3-inch squares from the corners of a rectangualr sheet of metal that is 4 inches longer than it is wide. If the box is to have a volume of 135 cubic inches, find the dimensions of the metal sheet.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A box is being constructed by cutting 3-inch squares from the corners of a rectangular sheet of metal that is 4 inches longer than it is wide.
If the box is to have a volume of 135 cubic inches, find the dimensions of the metal sheet.
:
Assume they mean an open box.
:
Cutting 3" squares from each corner make the box base dimensions 6" less than the metal sheet
We know the height of the box = 3" therefore:
Area of the base = = 45 sq/in
:
Let x = width of the metal
then we can say:
(x+4) = length of the metal
:
The base of the box dimensions: (x-6) by (x+4-6)
The area
(x-6)*(x-2) = 45
FOIL
x^2 - 2x - 6x + 12 = 45
x^2 - 8x + 12 - 45 = 0
x^2 - 8x - 33 = 0
Factors to
(x-11)(x+3) = 0
positive solution
x = 11" is the width of the metal sheet
then
11+4 = 15" is the length
:
:
See if that's true
(11-6) * (15-6) * 3 =
5 * 9 * 3 = 135 cu/in
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