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Expert: - 9/2/2010


Question
A 21m by 25m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 837m squared?

Answer
The total path has width w.
The are of this path would be 21w + 25w + 21w + 25w + 4w².
That is 4w² + 92w.

The total area is 21 x 25 = 525.
The area that is left over on the path is 837 - 525 = 312.

This gives us the equation 4w² + 92w = 312.
These terms are are divisible by 4, which gives w² + 23w = 78.

This comes down to solving the quadratic w² + 23w - 78 = 0.
Now b²-4ac is 23² + 4(78) = 529 + 312 = 841, and that is 29².

So the answer for w would be (-23+29)/2 = 3.



Now since the path is on both sides, add 6 to the length and width to get the new area.  This gives 27 x 31.  As can be seen, this is 620 + 217 = 837, so the answer is correct.

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