The perimeter of a sector which is 2/3 of a circle is 260cm find its radius

The perimeter of a sector is the sum of the lengths of its two radii and its arc length.
Let $r$ be the radius of the circle.
Let $L$ be the arc length of the sector.
The perimeter $P = 2r + L$.

The sector is $\frac{2}{3}$ of a circle.
The circumference of a full circle is $C = 2\pi r$.
The arc length $L$ of the sector is $\frac{2}{3}$ of the circumference:

We are given that the perimeter $P = 260$ cm. Substitute this and the expression for $L$ into the perimeter formula:

Factor out $r$ from the right side of the equation:

Find a common denominator for the terms inside the parenthesis:

Now, isolate $r$:

We can factor out 2 from the denominator:

Now, substitute the approximate value of $\pi \approx 3.14159$:

Rounding to two decimal places, the radius is 41.99 cm.

The radius of the sector is $\text{41.99 cm}$.