SOLUTION: A box with an open top is to be constructed by cutting 3-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a

Question 213543: A box with an open top is to be constructed by cutting 3-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 24in^3?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
L=2W
BOTTOM=(L-6)(W-6)
BOTTOM=LW-6W-6L+36
BOTTOM=2W*W-6W-6*2W+36
BOTTOM=2W^2-6W-12W+36
BOTTOM=2W^2-18W+36
VOLUME=3(2W^2-18W+36)
24=6W^2-54W+108
0=6W^2-54W+108-24
0=6W^2-54W+84
0=6(W^2-9W+14)
0=6(W-7)(W-2)
W-7=0
W=7 ANS. FOR THE WIDTH.
L=2*7=14 ANS. FOR THE LENGTH.
PROOF:
24=3(7-6)(14-6)
24=3*1*8
24=24
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