Will it be true to say that the perimeter of a square circumscribing a circle of radius $a \, cm$ is $8 a \, cm$? Give reasons for your answer.
(A) True.
Given,radius of the circle,$r = a \, cm$.
Therefore,the diameter of the circle,$d = 2 \times \text{radius} = 2a \, cm$.
Since the square circumscribes the circle,the side of the square is equal to the diameter of the circle.
Therefore,the side of the square $= 2a \, cm$.
Now,the perimeter of a square $= 4 \times \text{side} = 4 \times 2a = 8a \, cm$.
Hence,it is true that the perimeter of the square is $8a \, cm$.
Given,radius of the circle,$r = a \, cm$.
Therefore,the diameter of the circle,$d = 2 \times \text{radius} = 2a \, cm$.
Since the square circumscribes the circle,the side of the square is equal to the diameter of the circle.
Therefore,the side of the square $= 2a \, cm$.
Now,the perimeter of a square $= 4 \times \text{side} = 4 \times 2a = 8a \, cm$.
Hence,it is true that the perimeter of the square is $8a \, cm$.
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