Question

The area of equilateral ΔABC is 81√3 cm². Find the circum-radius of ΔABC. 

1. 6√2 cm
2. 6√3 cm
3. 3 cm
4. 9√3 cm

Answer 1

Correct Answer - Option 2 : 6√3 cm

Given:

Area of equilateral ΔABC = 81√3 cm²

Concepts used:

Area of equilateral triangle = √3/4 × (side)²

Circum-radius (R) of equilateral triangle = Side/√3

Calculation:

Area of equilateral triangle = √3/4 × (side)²

⇒ 81√3 cm² = √3/4 × (side)²

⇒ (Side)² = 81 × 4 cm²

⇒ Side = √324 cm = 18 cm

Circum-radius (R) of equilateral triangle = Side/√3

⇒ R = 18/√3 cm

⇒ R = 6√3 cm

∴ Length of circum-radius is equal to 6√3 cm.