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 perimeter be $P$. For Adu's square land: side $s = \frac{P}{4}$, Area $A_1 = s^2 = \frac{P^2}{16}$. For Amu's circular land: $2\pi r = P \implies r = \frac{P}{2\pi}$, Area $A_2 = \pi r^2 = \pi \left(\frac{P}{2\pi}\right)^2 = \frac{P^2}{4\pi}$. Ratio of areas $A_1 : A_2 = \frac{P^2}{16} : \frac{P^2}{4\pi} = \frac{1}{16} : \frac{1}{4\pi} = \frac{\pi}{4} = \pi : 4$.

Ratio of Land Areas

Explanation

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