SOLUTION: I need help with this word problem:My online HW is giving me one last try on this problem.
The width of a rectangular piece of cardboard is 7 inches less than the length. A square
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The width of a rectangular piece of cardboard is 7 inches less than the length. A square
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Question 681107: I need help with this word problem:My online HW is giving me one last try on this problem.
The width of a rectangular piece of cardboard is 7 inches less than the length. A square piece that measures 3 inches on each side is cut from the corner, than the sides are turned up to make a box with volume 360 inches^3. Find the length and width of the original piece of cardboard.
Thank you so much for looking at the problem. Found 2 solutions by Alan3354, ankor@dixie-net.com:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The width of a rectangular piece of cardboard is 7 inches less than the length. A square piece that measures 3 inches on each side is cut from the corner, than the sides are turned up to make a box with volume 360 inches^3. Find the length and width of the original piece of cardboard.
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Vol = 3*(L-6)*(W-6) = 360
L = W + 7
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3*(W+7-6)*(W-6) = 360
(W+1)*(W-6) = 120
W^2 - 5W - 126 = 0
(W+9)*(W-14) = 0
W = 14 (Ignore the -9)
L = 21
You can put this solution on YOUR website! The width of a rectangular piece of cardboard is 7 inches less than the length.
A square piece that measures 3 inches on each side is cut from the corner, then the sides are turned up to make a box with volume 360 inches^3.
Find the length and width of the original piece of cardboard.
:
Let L = the original length of the cardboard
Let W = the original width
:
"The width of a rectangular piece of cardboard is 7 inches less than the length."
W = L - 7
:
The removal of these 3" squares subtract 6" for the length and width
Box Length = (L-6)
Box Width = (W-6)
Replace W with (L-7)
(L-7) - 6 = (L-13) is the box width in terms of L
:
The height of the box will be 3 inches
:
The volume equation
3(L-6)(L-13) = 360
FOIL
3(L^2 - 13L - 6L + 78) = 360
divide both sides by 3
L^2 - 19L + 78 = 120
L^2 - 19L + 78 - 120 = 0
L^2 - 19L - 42 = 0
Factors to
(L - 21)(L + 2) = 0
the positive solution
L = 21" is the length of the original cardboard
and
W = 21 - 7
W = 14" is the width
:
:
Check this out
21 - 6 = 15" box length
14 - 6 = 8" box width
Vol: 15 * 8 * 3 = 360 cu/in
