Correct Answer - Option 4 : 14 cm
Given
The perimeter of a circle is 264 cm
Two sides of triangle = 21 cm and 12 cm
Area of triangle = 21 cm2
Concept
Circumradius (R) = (S1 × S2 × S3)/(4 × Δ )
Where,
S1 , S2 and S3 are sides of triangle
Δ = Area of triangle
Perimeter of circle = 2πR
Calculation
Perimeter = 2 × (22/7) × R
⇒ 264 = 2 × (22/7) × R
⇒ 6 × 7 = R
⇒ 42 = R
Now,
⇒ 42 = (21 × 12 × S3)/(4 × 21)
⇒ S3 = 14 cm.
∴ The third side of the triangle is 14 cm