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# Area of a Rectangle

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Just something interesting that I have known about for a long time. If you have a rectangle that is 2 inches wide by 1 inch tall, you have an area of 2 squared inches. If you have a rectangle that is 2.5 inches wide by .5 inch tall it is an area of 1.25 squared inches. However, both have a parimeter of 6 inches! I think that, say you had a loop of string that is 6 inches long, the way you get the most area out of it is having it in a triangle shape.

Noah

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• 4 weeks later...

Circle with radius 0.9549 will give you an area of 2.865.

Meaning what?

Eugene

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A circle with radius of 0.9549 inches has circumference (perimeter) 6 inches. Area of it is 2.865 inches squared, which is greater than the 1.618 inches squared of a equilateral triangle. This disproves what noah suggested, that a triangle gives the most area with a given perimeter.

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Ok. I saw this on a TV show when I was 8 or so. The other day I figured the rectangles but not a triangle.

Noah

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Thanks for the explanation; excuse my shortness.

Eugene