SOLUTION: The area of the rectangular piece of cardboard shown on the left is 198 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and tur
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Question 242218: The area of the rectangular piece of cardboard shown on the left is 198 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides. If the box is to have a volume of 196 cubic inches, find the length and width of the cardboard that must be used.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The area of the rectangular piece of cardboard shown on the left is 198 square inches.
The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides.
If the box is to have a volume of 196 cubic inches, find the length and width of the cardboard that must be used.
:
Area of the original piece of cardboard
L * W = 198 sq/in
L =
:
Volume L*W*H = 196 cu/in
(removing 2" squares reduces the length and width by 4", height = 2"
(L-4)*(W-4)*2 = 196
Simplify, divide both sides by 2
(L-4)*(W-4) = 98
FOIL
LW - 4L - 4W + 16 = 98
:
LW - 4L - 4W + 16 - 98 = 0
:
LW - 4L - 4W - 82 = 0
:
From the area equation, replace L with 198/W
*W - 4* - 4W - 82 = 0
Cancel W, mult by 4
198 - - 4W - 82 = 0
:
Mult by W to get rid of the denominator
198W - 792 - 4W^2 - 82W
:
Arrange as a quadratic equation
-4W^2 + 198W - 82W - 792 = 0
:
-4W^2 + 116W - 792 = 0
Divide by -2, simplify and change the signs
2W^2 - 58W + 396 = 0
This will factor
(2W - 22)(W - 18}) = 0
Two solutions
2W = 22
W = 11
and
W = 18
;
18" by 11" is the cardboard used
:
Check the area: 18 * 11 = 198
:
Check the vol of the box
(18-4)*(11-4)* 2 = 196
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