Question

Adu and Amu have bought two pieces of land on the Moon from an e-store. Both the pieces of land have the same perimeters, but Adu's piece of land is in the shape of a square, while Amu's piece of land is in the shape of a circle.

The ratio of the areas of Adu's piece of land to Amu's piece of land is:

Accepted Answer

D. Let the common perimeter be $P$. For Adu's square land: Side $s = \frac{P}{4} \implies 	ext{Area}_{Adu} = s^2 = \frac{P^2}{16}$. For Amu's circular land: Circumference $2\pi r = P \implies r = \frac{P}{2\pi} \implies 	ext{Area}_{Amu} = \pi r^2 = \pi \left(\frac{P}{2\pi}ight)^2 = \frac{P^2}{4\pi}$. Ratio of areas = $\frac{P^2/16}{P^2/4\pi} = \frac{4\pi}{16} = \frac{\pi}{4}$.

Area Ratio of Square and Circle of Equal Perimeter

Explanation

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