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)(r1)2θ1
where r1 is the radius,
θ1 is the angle in radians subtended by the arc at the center of the circle.
Similarly
Area of second sector = (1/2)(r2)2θ2
where r2 is the radius,
θ2 is the angle in radians subtended by the arc at the center of the circle.
It is given that:
(1/2)(r1)2θ1 = (1/2)(r2)2θ2
(r1)2θ1 = (r2)2θ2
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
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