Question 69

The perimeter(in metres) of a semicircle is numerically equal to its area (in square meters). The length of its diameter is (Take $$\pi = \frac{22}{7}$$)

Solution

Let radius of semi circle = $$r$$ metres

According to ques, Perimeter = Area

=> $$\pi r+2r=\frac{1}{2}\pi r^2$$

=> $$\pi+2=\frac{1}{2} \pi r$$

=> $$r=\frac{2\pi+4}{\pi}$$

=> $$r=2+4\times\frac{7}{22}$$

=> $$r=2+\frac{14}{11}=\frac{36}{11}$$

$$\therefore$$ Diameter = $$2\times\frac{36}{11}=6\frac{6}{11}$$ meters

=> Ans - (A)

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