The length of a rectangle is 6 cm more than its breadth and its perimeter is 100 cm. If the area of the rectangle is very nearly equal to the area of a circle, then what is the circumference of the circle?(Take $$\pi = \frac{22}{7}$$)

Let's assume the length and breadth of a rectangle are L and B respectively.

The length of a rectangle is 6 cm more than its breadth.

L = B-6    Eq.(i)

its perimeter is 100 cm.

2(L+B) = 100

L+B = 50    Eq.(ii)

Put Eq.(i) in Eq.(ii).

B-6+B = 50

2B-6 = 50

2B = 50+6 = 56

B = 28 cm

Put the value of 'B' in Eq.(i).

L = 28-6

L = 22 cm

If the area of the rectangle is very nearly equal to the area of a circle.

$$L\times\ B\ =\ \pi\ \times\ \left(radius\right)^2$$

$$22\times\ 28\ =\ \frac{22}{7}\ \times\ \left(radius\right)^2$$

$$28\ =\ \frac{1}{7}\ \times\ \left(radius\right)^2$$

$$196=\left(radius\right)^2$$

radius = 14 cm

Circumference of the circle = $$2\times\ \pi\ \times\ radius$$

= $$2\times\frac{22}{7}\times14$$

= $$2\times22\times2$$

= 88 cm