Question

If the circumference of a circle and the perimeter of a square are equal , then
(a) Area of the circle = Area of the square (b) Area of the circle < Area of the square
(c) Area of the circle > Area of the square (d) nothing definite can be said

Answer 1

Circumference of the circle = Perimeter of the square
$$\begin{gathered} 2\mathrm{\pi }r=4a \\ \mathit{\Rightarrow }r\mathit{=}\frac{\mathit{2}\mathit{a}}{\mathit{\pi }} \end{gathered}$$
Now area of the circle = $\mathrm{\pi }{r}^2=\mathrm{\pi }{\left(\frac{2\mathrm{a}}{\mathrm{\pi }}\right)}^2=\frac{4{\mathrm{a}}^2}{\mathrm{\pi }}$
Area of the square = a²
So, the area of the circle > area of the square
Hence, the correct answer is option (c).