Sometimes what is possible is what is impossible

Geometry Level 1

A shape has perimeter X cm X \text{ cm} and area Y cm 2 Y \text{ cm}^2 . Is it possible that X > Y X>Y ?

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Rex Holmes by Rex Holmes , 17, USA

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2 solutions

Mahdi Raza
Jun 3, 2020

Consider a square with side 1 1

X = 4 × 1 = 4 Y = ( 1 ) 2 = 1 \begin{aligned} X &= 4\times 1 &=4 \\ Y &= (1)^2 &= 1 \end{aligned}

X > Y \boxed{X > Y}

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Rex Holmes
Sep 12, 2016

consider a square with side length 3. 3X3=9 but 3+3+3+3=12 therefore in a square like this, p-a=3

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http://mathforum.org/library/drmath/view/60402.html

ma pm - 4 years, 9 months ago

they're not comparable

ma pm - 4 years, 9 months ago

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how are they not comparable?

Rex Holmes - 4 years, 9 months ago

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They aren't comparable because you can change the ratio between the two by either using larger or smaller units. In a square, area is a side multiplied by itself while perimeter is 4 times a side.

Casey A - 4 years, 9 months ago

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