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

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Question 167613: A box with an open top is to be constructed by cutting 3-inch squares from a rectangular sheet of tin whose length is twice its width. What are the dimensions of the sheet of tin that results in a box having a volume of 60 cubic inches?
Answer by nerdybill(7384) About Me  (Show Source):
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A box with an open top is to be constructed by cutting 3-inch squares from a rectangular sheet of tin whose length is twice its width. What are the dimensions of the sheet of tin that results in a box having a volume of 60 cubic inches?
.
Let w = width of rectangular sheet
then
2w = length of rectangular sheet
.
With the 3-inch cut made we would have:
w-6 = width after making the cuts
2w-6 = length after making the cuts
.
3(w-6)(2w-6) = 60
(w-6)(2w-6) = 20
2(w-6)(w-3) = 20
(w-6)(w-3) = 10
w^2 - 9w + 18 = 10
w^2 - 9w + 8 = 0
(w-8)(w-1) = 0
w = {1, 8}
.
We can throw away 1 because if you cut 3-inch it'll be negative.
So,
dimensions:
8 in. by 16 in.