SOLUTION: I would really appreciate help with this problem. Thanks! I submitted this question once but I am still not sure of the answer. Could you also walk me through checking the answer

Question 277382: I would really appreciate help with this problem. Thanks! I submitted this question once but I am still not sure of the answer. Could you also walk me through checking the answer.
Shipping: A shipping box is reinforced with steel bands in all three directions. A total of 20.5 feet of steel tape is to be used, with 6 inches of waste because of a 2 inch overlap in each direction. If the box has a square base and a volume of 2 cubic feet, find the dimensions.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A shipping box is reinforced with steel bands in all three directions.
A total of 20.5 feet of steel tape is to be used, with 6 inches of waste because of a 2 inch overlap in each direction.
:
Find total length of the bands. A box with a square base, dimensions x by x by h
horizontal band: 4x
two other bands: 2(2x + 2h) = 4x + 4h
Total of all three bands: 8x + 4h
8x + 4h = 20; subtracted the 6" used for overlap
Simplify divide by 4
2x + h = 5
h = (5-2x)
:
If the box has a square base and a volume of 2 cubic feet, find the dimensions.
x^2 * h = 2
Replace h
x^2 * (5-2x} = 2
-2x^3 + 5x^2 - 2 = 0
:
We can save a lot of work by plotting this equation

Find the exact x intercepts points, using a graphing calc
x = 2.313,
and
x = .7576 ft,
:
Find h, when x = 2.313 the dimensions of the square base
h = 5-2x
h = 5-2(2.313)
h = .374 ft is the height
and
Find h, when x = .7576 ft the dimensions of the square base
h = 5-2(.7576)
h = 3.4848 ft is the height
:
:
Check solutions by finding the volume for each solution set:
base^2 * height =
.7576^2 * 3.4848 = 2.000
and
2.313^2 * .374 = 2.000

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