If the perimeter of a circle is equal to that of a square, then ratio of their areas is:

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\frac{4}{π}

\frac{24}{π}

\frac{3}{π}

\frac{6}{π}

answer is A.

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Detailed Solution

Given that, the perimeter of a circle is equal to that of a square.
Let radius of circle be r and side of a square be a.
Perimeter of a circle (circumference) = 2πr
Perimeter of a square = 4a
Perimeter of circle=Perimeter of square
2πr=4a

\Rightarrow \frac{r}{a} = \frac{4}{2 πr}

\Rightarrow \frac{r}{a} = \frac{2}{π}

Now,

\frac{Areaofcircle}{Area of square} = \frac{π r^{2}}{a^{2}}

\Rightarrow π (\frac{r}{a})^{2}

\Rightarrow π {(\frac{2}{π})}^{2}

\Rightarrow \frac{4}{π^{2}} \times π

\Rightarrow \frac{4}{π}

Thus, the ratio of area of a circle to that of a square is

\frac{4}{π}

.
Therefore, required answer is 1.

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