Math Is Fun Forum

victoria manzanita

Member

Registered: 2010-03-24

Posts: 1

same area different perimeter

could somebody help me in answering this ? the area of a rectangle is 100 sq. inches the perimeter of the rectangle is 40 inches a second rectangle has the same area but a different perimeter is the second rectangle a sq. explain why or why not

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: same area different perimeter

Hi victoria manzanita;

Something is wrong with the question:

A= L * W = 100 solve for W = 100 / L

P = 2L + 2W = 40

2L + 200 / L = 40

2L^2  - 40L + 200 = 0

L = 10 , L = 10 Solving for W = 10, so the first one is a square. The only way the second one could be a square is if it was eactly the same as the first one, but it can't be because it has a different perimeter.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
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White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: same area different perimeter

Obviously, there are infinite number of the rectangles with the area of 100 square inches. And only one of them is square, that is a rectangle with sides equal 10", and perimeter 4*10"=40". Therefore, the 'first' rectangle is a square. Since there are can be only square between all rectangles with same areas, we conclude that 'second' rectangle is not a square.