Riddle: Which One Of Them Would Have A Greater Area?

Answer: Option B

Explanation:

Let us assume;
s is the side length of the square
r is the radius of the circle.

Perimeter of square = 4s
Perimeter or circumference of Circle = 2π r

From the given information we can write;

4s = 2π r.

Therefore;
s=π r/2. ——–(1)

Now we know;

Area of square = s^2 &
Area of circle = π r^2

Substituting value of s from (1) we get;

s^2 = π ^2 x r^2/4 – – (a)

and

the area of the circle π x r^2. – – (b)

Now to compare let’s just equate them to know which one has the larger area.

Now, let’s say, (a) = (b)
Area of Square = Area of Circle

π ^2 x r^2/4 = π  x r^2
(r^2 and a π gets cancelled on both sides)

We get,
π  /4 = 1

As we know that,
π  /4 is less than 1
π /4 < 1

Hence, Area of Square < Area of Circle.

Thus, the area of Circle is greater.

So, Option (B) is right.