Question 130

Area of circle is equal to the area of a rectangle having perimeter of 50 cms. and length more than the breadth by 3 cms. What is the diameter of the circle?

Solution

Let the breadth of rectangle be $$x$$ cm

=> Length of rectangle = $$(x + 3)$$ cm

Now, perimeter = $$2 (x + x + 3) = 50$$

=> $$2x + 3 = 25$$

=> $$x = \frac{22}{2} = 11$$

Thus, breadth = 11 cm and length = 14 cm

$$\because$$ Area of circle = Area of rectangle

=> $$\pi r^2 = 14 \times 11$$

=> $$r^2 = \frac{14 \times 11 \times 7}{22}$$

=> $$r = \sqrt{7 \times 7} = 7$$ cm

$$\therefore$$ Diameter = 2 * 7 = 14 cm

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