If the circumference of a circle and the perimeter of a square are equal, then ______.

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If the circumference of a circle and the perimeter of a square are equal, then Area of the circle > Area of the square. Explanation: According to the given condition, Circumference of a circle = Perimeter of square 2$\pi$r = 4a ...[Where r and a are radius of circle and side of square respectively] $\Rightarrow$ $\frac{22}{7}$ "r" = 2a $\Rightarrow$ 11r = 7a $\Rightarrow$ a = $\frac{11}{7}$ "r" $\Rightarrow$ r = (7"a")/11 ...(i) Now, Area of circle, A1 = $\pi$r2 = $\pi$((7"a")/11)^2 ...[From equation (i)] = $\frac{22}{7}$ xx (49"a"^2)/121 = (14"a"^2)/11 ...(ii) And Area of square, A2 = (a)2 ...(iii) From equations (ii) and (iii), A1 = $\frac{14}{11}$ "A"_2 $\therefore$ A1 > A2 Hence, Area of the circle > Area of the square.

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