Question

The area of equilateral ΔPQR is 36√3 cm². Find the circumradius of ΔPQR.
1. 4 cm
2. 2.3 cm
3. 4√3 cm
4. 1.5 cm

Answer 1

Correct Answer - Option 3 : 4√3 cm

Given:

Area of equilateral ΔPQR = 36√3 cm²

Concepts used:

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

Circumradius (R) of equilateral triangle = Side/√3

Calculation:

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

⇒ 36√3 cm² = (√3/4) × (Side)²

⇒ (Side)² = 36 × 4 cm²

⇒ Side = √144 cm

⇒ Side = 12 cm

Circumradius (R) of equilateral triangle = Side/√3

R = 12/√3 cm

⇒ R = 4√3 cm

∴ Length of circumradius is equal to 4√3 cm.