A circle, made of wire, of diameter 49 cm is formed into a rectangle whose sides are in the ratio 7 : 4. Find the area of the rectangle. [Take π = $$\frac{22}{7}$$​]

Correct option is A

Given:

Diameter of the circle = 49 cm
Radius = $$\frac{49}{2}$$​= 24.5 cm
Ratio of rectangle’s sides = 7 : 4
π $$= \frac{22}{7}$$​​

Formula Used:

Circumference of circle = 2πr

Perimeter of rectangle = 2(l + b)

Solution:

If sides are in ratio 7 : 4, let l = 7x, b = 4x

Circumference =$$2 \times \frac{22}{7} \times 24.5 = 2 \times \frac{22}{7} \times \frac{49}{2} = 154 \text{ cm}$$​

2(l + b) = 154

2(7x + 4x) = 154

2(11x) = 154

11x = 77

x = 7

l = 7x = 49 cm

b = 4x = 28 cm

Area = $$l \times b = 49 \times 28 = 1372 \text{ cm}^2$$​​