The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

(B) The statement is False.
Let the radii of the two circles be $r_1$ and $r_2$,and the lengths of the arcs be $l_1$ and $l_2$. Given that the arc lengths are equal,we have $l_1 = l_2 = l$.
The formula for the length of an arc is $l = r \theta$,where $\theta$ is the angle in radians.
The area of a sector is given by $A = \frac{1}{2} r^2 \theta$.
Since $l = r \theta$,we can write $\theta = \frac{l}{r}$.
Substituting this into the area formula,we get $A = \frac{1}{2} r^2 (\frac{l}{r}) = \frac{1}{2} rl$.
For two different circles with the same arc length $l$,the areas are $A_1 = \frac{1}{2} r_1 l$ and $A_2 = \frac{1}{2} r_2 l$.
Since the circles are different,their radii $r_1$ and $r_2$ are not equal $(r_1 \neq r_2)$.
Therefore,$A_1 \neq A_2$. Thus,the areas are not necessarily equal.