The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field?
Take $$\pi = \frac{22}{7}$$​

Correct option is C

Given:

Rectangle sides: 169 m and 154 m.

Area of rectangle = Area of circle.

Use $$\pi=\dfrac{22}{7}$$​​

Find circumference of the circle.

Formula Used:

Area (rectangle): A$$_r = l \times b$$​​

Area (circle): A$$_c=\pi r^2$$​.

Circumference (circle): C=$$2\pi r$$​.

Solution:
Area of rectangle =$$169 \times 154 = 26026\ \text{m}^2$$​​
Set equal: $$\pi r^2$$​ = 26026

​$$r^2=\dfrac{26026}{\pi}=\dfrac{26026}{\frac{22}7}=26026 \times \dfrac{7}{22}=8281$$​​
So r$$=\sqrt{8281}=91\text{ m}.$$​​

Circumference C$$=2\pi r=2\times \dfrac{22}{7}\times 91=\dfrac{44}{7}\times 91=44\times 13=572\text{ m}$$​​