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MCQ

Fill in the Blanks

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

#### Options

13 : 22

14 : 11

22 : 13

11 : 14

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#### Solution

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is **14 : 11**.

**Explanation:**

Let radius of circle be r and side of a square be a.

Perimeter of a circle = Perimeter of a square

∴ `2pir = 4a`

⇒ `a = (pir)/2` .....(i)

Now, `"Area of circle"/"Area of square" = (pir^2)/(a)^2 = pi^2/((pir/2)^2` ......[From equation (i)]

= `(pir^2)/((pi^2r^2)/4) = 4/pi`

= `4/(22/7) = 28/22`

= `14/11`

Concept: Area of Circle

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