SOLUTION: a community flower garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What ill be the

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Question 503498: a community flower garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What ill be the width of the pathway?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Borders are interesting because you have to remember that you have to pave the 4 corners.
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The area of the garden = 12*16 = 192 square meters.
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Then you add the border with width 'x'.
So,
Length is now L + 2x
Width is now W + 2x
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We are told:
(L+2x)(W+2x) = 285
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(12+2x)(16+2x) = 285
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192 +24x +32x +4x^2 = 285
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4x^2 + 56x + 192 = 285
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4x^2 + 56x - 93 = 0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B56x%2B-93+=+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=%2856%29%5E2-4%2A4%2A-93=4624.

Discriminant d=4624 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-56%2B-sqrt%28+4624+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2856%29%2Bsqrt%28+4624+%29%29%2F2%5C4+=+1.5
x%5B2%5D+=+%28-%2856%29-sqrt%28+4624+%29%29%2F2%5C4+=+-15.5

Quadratic expression 4x%5E2%2B56x%2B-93 can be factored:
4x%5E2%2B56x%2B-93+=+4%28x-1.5%29%2A%28x--15.5%29
Again, the answer is: 1.5, -15.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B56%2Ax%2B-93+%29

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You cannot have a negative width, so the border is 1.5 m.
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Always check your work.
L = 12 + 2(1.5) = 15
W = 16 + 2(1.5) = 19
15*19 = 285
Correct.
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Answer: The border is 1.5 meters wide.
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Done.