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Question
Find the radius of a circle whose perimeter and area are numerically equal.
Solution
Let the radius of the required circle be r.
Now, Area of circle = Perimeter of the circle
⇒ πr2 = 2π × r
⇒ r2 = 2r
⇒ r2 - 2r =0
⇒ r(r - 2) = 0
⇒ r - 2 = 0 [∴ r ≠ 0]
⇒ r = 2 units
Hence, the radius of the circle is 2 units.
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