Consider statement A alone.

Length of the equal sides of the triangle is 5 cm.

where

*a* represents the length of the equal side and

*b* represents the length of the third side.

On squaring both the sides we get,

3600 × 16 =

*b*^{2}( 676 −

*b*^{2} )

∴

*b*^{4} − 676

* b*^{2 }+ 57600 = 0

∴

*b*^{2} = 576 or

*b*^{2} = 100

As the length of the side of a triangle cannot be negative.

∴

*b* = 24 or

*b* = 10

∴ The length of the third side of the triangle can be 24 cm or 10 cm

∴ We get two values for the semi-perimeter of the triangle.

Area of the triangle =

*r* ×

*S*

where

*r* represents the radius of the incircle drawn in the triangle and

*S* represents the semi-perimeter of the triangle.

∵ We get two values for the semi-perimeter of the triangle, we will get two values for the inradius and thus two values for the area of the incircle.

∴ Using statement A alone, we cannot find the exact area of the incircle.

Consider statement B alone.

Distance of the meeting point of the two medians drawn on the equal sides of the triangle from their respective opposite vertices is 4 cm from the non equal side of the triangle.

Meeting point of the two medians is the centroid of the triangle.

∴ Distance of the centroid from the non equal side of the triangle is 4 cm.

The centroid divides the median in the ratio of 2:1

∴ Length of the median will be 12 cm which is also the height of the triangle.

∴ Length of the base of the triangle = 10 cm

∴ 3600 × 16 = 100 ( 4

*a*^{2} − 100 )

∴ 400

*a*^{2} = 67600

∴

*a*^{2 }= 169

As the length of the side of a triangle cannot be negative.

∴

*a *= 13 cm

∴ Length of the equal sides of the isosceles triangle is 13 cm.

Area of the triangle =

*r* ×

*S*

Since the semiperimeter can be uniquely determined, the inradius can be uniquely determined.

∴ Area of the incircle can be uniquely determined.

∴ Statement B alone is sufficient to answer the question.

Hence, option 2.