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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

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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.

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