Area = Perimeter

It is quite simple to figure this out.

According to the question, area of the sector = perimeter of the arc.

The formula to find the area of the sector if the angle subtended by it is $\theta$ is,

$\displaystyle\frac{\theta πr^{2}}{360}$ . . . . . . . . (i).

And, similarly for the perimeter of the arc, the formula is,

$\displaystyle \frac{\theta ×2πr}{360}$ . . . . . . . . . .(ii).

Equating, (i) and (ii) we get,

$\displaystyle \frac{\theta πr^{2}}{360} = \displaystyle \frac{\theta× 2πr}{360}$

Or, $πr^{2} = 2πr$

Or, $r = \boxed {2}$

The question should have length of arc .

Length of Arc = $R \times \theta$

Area of Sector = $\frac{1}{2}\times R^2\times \theta$

(ANGLE IN RADIAN)

Thus Equating these we get:

R = 2.