Use your mathematical and logical skills to solve this riddle.
A square and a circle have the same perimeter.
In such a case, which one of them would have a greater Area?
C. Both have same area.
D. Insufficient Data.
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Answer: Option B
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.
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)
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)
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.