Question

If the area of a circle is equal to the area of a square, then the ratio of their perimeters is:

• A. \( 1:1 \)
• B. \( 2:\pi \)
• C. \( \pi:2 \)
• D. \( \sqrt{\pi}:2 \)

Hint:

When comparing perimeters or areas, always **express both in terms of the same variable**.

Answer 1

The Correct Option is C

Let the radius of the circle be \( r \) and the side of the square be \( s \).
\[ \pi r^2 = s^2 \] \[ s = \sqrt{\pi r^2} = r\sqrt{\pi} \] Perimeter of Circle:
\[ P_C = 2\pi r \] Perimeter of Square:
\[ P_S = 4s = 4r\sqrt{\pi} \] Taking the ratio:
\[ \frac{P_C}{P_S} = \frac{2\pi r}{4r\sqrt{\pi}} = \frac{\pi}{2} \]