Question 681107
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