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Question 59
The perimeter of a square and a circle are same. If the area of the circle is 2464 $$cm^2$$, then what will be the area of the square?
Solution
Given, Area of circle = $$2464 cm^2$$
$$\dfrac{22}{7}\times r^2 = 2464$$ where r = radius of circle
=> $$r^2 = 784$$
=> $$r = 28 cm$$
Circumference of circle = $$2\times\dfrac{22}{7}\times28 = 176 cm$$
Circumference of circle = Perimeter of square = 176 cm
4a = 176 => a = 44 cm. where a = side of the square
Therefore, Area of the square $$= 44^2 = 1936 cm^2$$
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