Why a Square Maximizes Area/PerimeterDate: 07/24/2002 at 10:21:44 From: Elizabeth Subject: area and perimeter I need to come up with a rectangle with an area greater than 16 ft. squared, and a perimeter of 16 ft. Date: 07/24/2002 at 12:27:34 From: Doctor Ian Subject: Re: area and perimeter Hi Elizabeth, Has someone led you to believe that this would be possible? A square with perimeter 16 ft has an area of 16 ft^2: 4 +---+ | | 4 +---+ Suppose we keep the same perimeter, but use another shape. To do this, we would have to reduce the width by some amount, x, and increase the length by the same amount: 4-x +--+ | | | | 4+x +--+ Now the perimeter is still 16 feet, but the area is A = (4+x)(4-x) = 4^2 - x^2 = 16 - x^2 square feet. Which is to say, _any_ change we make, from a square to a non-square rectangle, will result in a smaller area. Does that make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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