SOLUTION: A 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 will be the width of the pat

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Question 779240: A 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 will be the width of the pathway?

I know that the area of the path is 93, but what do I do with that???
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A 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 will be the width of the pathway?
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Draw a rectangle within a rectangle.
The dimensions of the inner rectangle are 12 by 16 meters
The dimensions of the outer rectangle are 12+2x by 16+2x
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Equations:
(12+2x)(16+2x) = 285 sq. meters
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4(6+x)(8+x) = 285
4[x^2 + 14x + 48) = 285
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x^2 + 14x + 48 = 71.25
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x^2 + 14x - 23.25 = 0
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x = 1.5 ft is the width of the pathway.
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Cheers,
Stan H.
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