Question 146

Area of a rectangle is equal to the area of the circle whose radius is 21 cms. If the length and the breadth of the rectangle are in the ratio of 14 : 11 respectively, what is its perimeter?

Solution

Radius of circle = 21 cm

=> Area of circle = $$\pi r^2$$

= $$\frac{22}{7} \times 21 \times 21 = 1386 cm^2$$

Thus, area of rectangle = $$1386 cm^2$$

Let length and breadth of rectangle be $$14x$$ and $$11x$$ respectively.

=> Area = $$14x \times 11x = 1386$$

=> $$x^2 = \frac{1386}{154} = 9$$

=> $$x = \sqrt{9} = 3$$ cm

$$\therefore$$ Perimeter = $$2 (14x + 11x)$$

= $$2 \times 25x = 50x$$

= $$50 \times 3 = 150$$ cm

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