1.

The Circumference of a circle is 264 cm, if a triangle PQR is inscribe in the circle having two sides are 21 cm and 12 cm and the area of triangle is 21 cm2. Then find the third side of the triangle .1. 28 cm2. 22 cm3. 24 cm4. 14 cm

Answer» 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



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