We know length of an arc is = angle subtended in radians * radius of the circle  Therefore in our case Length of the arc = x*r Also, area of sector = $$frac{ extrm{angle subtended in radians}}{2}$$ * $$radius^2$$ Therefore in our case area of sector = $$frac{x}{2}$$ * $$r^2$$ Also given that  area of sector = length of an arc^2 Therefore $$x^2*r^2$$ = $$frac{x}{2}$$ * $$r^2$$ Solving we get x= 0.5 Therefore our answer is Option "A"