Question

The Circumference of a circle is 528 cm if a triangle PQR is inscribed in the circle having two sides are 28 cm and 12 cm and the area of the triangle is 21 cm². Then find the third side of the triangle.
1. 21 cm
2. 12 cm
3. 10.5 cm
4. 44 cm

Answer 1

Correct Answer - Option 1 : 21 cm

Given

The perimeter of a circle is 528 cm

Two sides of triangle = 28 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

⇒ 528 = 2 × (22/7) × R

⇒ 12 × 7 = R 

⇒ 84 = R

Now, 

⇒ 84 = (28 × 12 × S₃)/(4 × 21)

⇒ S₃ = 21 cm.

∴ Third side of the triangle is 21 cm