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| Math Central | Quandaries & Queries |
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Question from Jin: I have a large square pond set inside a square garden: both the pond and the garden have sides which are a whole number of metres, and outside the pond, the garden is grassed over. The area covered by grass is 188 square metres.
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Hi Jin,
I can help get you started.
Here is my sketch of the garden and pond. The garden measures $x$ metres on a side and the pond measures $y$ metres on a side. $x$ and $y$ are both whole numbers.
The area of the grass is the area of the $x$ by $x$ square minus the area of the surface of the pond. Thus
\[x^2 - y^2 = 188\]
Can you complete the problem now?
Write back if you need more assistance,
Penny
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