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Geometry Level 1

It is possible to have a shape such that its perimeter is numerically equal to its area?

No Yes

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5 solutions

Ryan Shi
Sep 13, 2016

Let P = P = perimeter of a square, A = A = area of a square and s = s = side

P = 4 s P = 4s

A = s 2 A = s^2

If P = A P = A , then s 2 = 4 s s^2 = 4s

s 2 4 s = 0 s^2 - 4s = 0

s ( s 4 ) = 0 s(s - 4) = 0

H e n c e Hence s = 0 , s = 4 s = 0, s = 4 .

As s = 4 s = 4 is a solution of a square ( s = 0 s = 0 can be ignored), and a square is a shape, regardless of all other shapes the answer must be T R U E TRUE

There's a conceptual mistake in this question! A perimeter is measured as length thus in, say, meters, and the area in sq. Meters. They can never de equal! E. Cruz

Eduardo Cruz - 4 years, 9 months ago

Can you show that no matter what the shape is, we can always find a suitable case where perimeter = area? E.g. what if we were considering an equilateral​ triangle?

Calvin Lin Staff - 4 years, 8 months ago
Viki Zeta
Sep 12, 2016

For every polygon, there is a possibility that area is same as perimeter.

Take for example, a square with length 4, area = perimeter = 16 .

Take a equilateral triangle with length a = 3 12 a = \dfrac{\sqrt[]{3}}{12} , area = perimeter = 0.577 0.577\ldots

Rex Holmes
Sep 12, 2016

consider a square with side length 4. 4X4=16. 4+4+4+4=16. Therefore p-a=0

Tran Hieu
Sep 19, 2016

Actually if you consider the unit of measurement, and ignore all line, then the answer must be false.

Steven Chase
Sep 14, 2016

A circle with radius = 2 also works

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