Area=Perimeter

Geometry Level 3

A square's perimeter in inches is equal to its area in square inches.

A circle's circumference in inches is equal to its area in square inches.

Compare the two quantities:

$A.$ The diameter of the circle.

$B.$ The side length of the square.

A > B

Not enough information

A= B

A < B

1 solution

Hana Wehbi
Aug 4, 2017

The perimeter of the square = to its area $\implies 4s = s^2 \implies s^2- 4s =0 \implies s(s-4) = 0 \implies s= 4 \ in$ , where $s$ is the side length of the square.

The area of the circle = its circumference $\implies \pi r^2 = 2\pi r \implies r = 2 \implies d=4 \ in$ , where $r$ is the radius of the circle and $d$ is its diameter.

Thus $A = B.$

Area=Perimeter

1 solution

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