SOLUTION: With the lid closed, a "take out" box used by a restaurant has a volume of 121 cubic inches. Its length l equals its width w. A strip of tape is wrapped around the box to keep it c

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Question 168362: With the lid closed, a "take out" box used by a restaurant has a volume of 121 cubic inches. Its length l equals its width w. A strip of tape is wrapped around the box to keep it closed. The length of the tape measures 20 inches, which is 1 inch more than the shortest distance around the box. Find the dimenstions of the box.
I would really appreciate all steps as I know he will have this on an exam and I want to be able to show all the work.
Thank you for the time you take to help me out.
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The problem says l+=+w
If I call the height h, then the
volume will be V+=+l%2Aw%2Ah and since l+=+w
V+=+w%5E2%2Ah
It is given that V+=+121 in3
121+=+w%5E2%2Ah
The length of the tape measures 20 inches,
which is 1 inch more than the shortest
distance around the box.
So, the distance around the box is 19in
The box has a square base with sides = w
so the distance around the bnox = 4w
4w+=+19
w+=+19%2F4
121+=+w%5E2%2Ah
121+=+%2819%2F4%29%5E2%2Ah
Now solve for h
h+=+121+%2F+%28361%2F16%29
Now find h and solve for V
Hope I got it right- I think so

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
With the lid closed, a "take out" box used by a restaurant has a volume of 121 cubic inches.
Its length l equals its width w. A strip of tape is wrapped around the box to keep it closed.
The length of the tape measures 20 inches, which is 1 inch more than the shortest distance around the box. Find the dimensions of the box.
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l = w
Nothing is said about the height; I'm going to assume its height is "w".
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A wrap-around is w+w+w+w long
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Inequality:
tape = 4w+1 inches
20 = 4w+1
19 = 4w
w = (19/4) inches
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Cheers,
Stan H.