Calculating Circle Circumference

The radius of the circle is given as $r = 21$ cm.

The formula for the circumference ($C$) of a circle is $C = 2 \pi r$. Using the approximation $\pi \approx \frac{22}{7}$, we calculate the circumference:

$C = 2 \times \frac{22}{7} \times 21 \text{ cm}$

$C = 2 \times 22 \times 3 \text{ cm}$

$C = 132 \text{ cm}$

Finding Triangle Side Length

The problem states that the circumference of the circle equals the perimeter of an equilateral triangle.

The perimeter ($P$) of an equilateral triangle with side length $s$ is $P = 3s$.

Equating the circumference and the perimeter:

$C = P$

$132 \text{ cm} = 3s$

To find the side length $s$, divide the perimeter by 3:

$s = \frac{132 \text{ cm}}{3}$

$s = 44 \text{ cm}$

The length of the side of the equilateral triangle is 44 cm.