# The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why

**Solution:**

We know that

Area of first sector = (1/2)(r_{1})^{2}θ_{1}

where r_{1} is the __radius__,

θ_{1} is the angle in radians subtended by the arc at the center of the circle.

Similarly

Area of second sector = (1/2)(r_{2})^{2}θ_{2}

where r_{2} is the radius,

θ_{2} is the angle in radians subtended by the arc at the center of the circle.

It is given that:

(1/2)(r_{1})^{2}θ_{1} = (1/2)(r_{2})^{2}θ_{2}

(r_{1})^{2}θ_{1} = (r_{2})^{2}θ_{2}

It depends on angle subtended at the radius and the centre

The arc length depends on radius of the circle

So it is not necessary that the corresponding __arc lengths__ are equal

Therefore, the statement is false.

**✦ Try This:** The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 10**

## The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why

**Summary:**

The statement “The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal” is false

**☛ Related Questions:**

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