SOLUTION: Volume of a rectangular Chinese box: The volume of this box is 192 cu. units. Find its length and width.

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Question 182368This question is from textbook Developmental Mathematics
: Volume of a rectangular Chinese box: The volume of this box is 192 cu. units. Find its length and width. This question is from textbook Developmental Mathematics

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of a rectangular Chinese box: The volume of this box is 192 cu. units. Find its length and width.
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Not sufficient information.
192 = 2*4*24
192 = 4*6*8 and other combinations.
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Received additional info, the box is 4 by x by (x+2)
4*x*(x+2) = 192 (that looks familiar, 4 by 6 by 8, but I'll work it out)
x*(x+2) = 48
x%5E2+%2B+2x+-+48+=+0
(x-6)*(x+8) = 0
x = 6 (Ignore the -8, too difficult to construct)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-48+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-48=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%282%29-sqrt%28+196+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B2x%2B-48 can be factored:
1x%5E2%2B2x%2B-48+=+%28x-6%29%2A%28x--8%29
Again, the answer is: 6, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-48+%29