A) Their area are equal
B) Area of circle is larger
C) Area of square is larger
D) None of these
Correct Answer: B
Solution :
We are given that, the perimetre of the circle is equal to the perimetre of square. \[\therefore \] Let ?r? be the radius of circle and ?a? be the side of square \[\therefore \] \[2\pi \,r=4a\Rightarrow a=\frac{\pi \,r}{2}\] \[\therefore \] Area of square \[\Rightarrow \] \[{{a}^{2}}=\frac{{{\pi }^{2}}{{r}^{2}}}{4}\] and area of circle = \[\pi \,{{r}^{2}}\] \[\therefore \] \[\frac{\text{Area of circle}}{\text{Area of square}}=\frac{\pi \,{{r}^{2}}}{{{\pi }^{2}}{{r}^{2}}/4}=\frac{4}{\pi }>1\]. Thus, area of circle is larger than area of square.
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