SOLUTION: I would really appreciate help with this problem. Thanks! Shipping: A shipping box is reinforced with steel bands in all three directions. A total of 20.5 feet of steel tape i

Question 276249: I would really appreciate help with this problem. Thanks!
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.
If you could also show me how to check the answer I would really appreciate it.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
look at or think about a wrapped box

each dimension (width, depth, height) has 4 lengths of tape (bands)

subtracting the 6 inch waste ___ 4w + 4d + 4h = 20 ___ w + d + h = 5

the base is square, so ___ w = d ___ substituting ___ 2w + h = 5 ___ h = 5 - 2w

the volume is 2 ___ w * d * h = 2 ___ substituting ___ w^2 * h = 2 ___ w^2 (5 - 2w) = 2 ___ 0 = 2w^3 - 5w^2 + 2

when w = 1, the value of the expression is -1
___ when w = 1/2, the value of the expression is 1

you can test between these points to find a suitable value for w (this will also be the value for d)
HINT: should be close to 3/4

you can then substitute to find h
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