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# Circle Geometry help

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A piece of string fits exactly once around the perimeter of a square whose area is 144. Rounded to the nearest whole number, what is the area of the largest circle that can be formed from the piece of string?

Thanks

Jan 25, 2022

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We know the circumference of the circle = the perimeter of the square which is  $$\sqrt{144} =12\times4=48$$ (you get 12 and 12 x 4 =48)

$$2\pi r=48$$

$$\pi r=24$$

$$r=\frac{24}{\pi}$$

$$\pi\times\frac{24}{\pi}^2=\frac{576}{\pi}$$

$$576\pi$$ is about $$183$$

so 183.

Jan 25, 2022