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The greatest area is attained when the rectangle is, in fact, a square. Then it has sides of 5 cm and an area of 25 cm2. If you are not permitted to have a square then the answer is as close to 25 cm2 as you can get without actually getting there. So, more than 24.99, more than 24.99999 etc but never quite 25.

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Q: What is the greatest area for a rectangle with perimeter 20cm?
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