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The area of incircle of an equilateral triangle is 154 cm². The perimeter of the triangle is
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Given:
– Area of incircle = 154 cm².
Step 1: Find radius of incircle.
πr² = 154 ⇒ (22/7)r² = 154 ⇒ r² = 49 ⇒ r = 7 cm.
Step 2: Relate radius to side of equilateral triangle.
r = (a√3)/6 ⇒ 7 = (a√3)/6 ⇒ a = 42/√3 = 14√3 cm.
Step 3: Find perimeter.
Perimeter = 3a = 3 × 14√3 ≈ 3 × 14 × 1.732 ≈ 72.7 cm.
This question related to Chapter 11 Mathematics Class 10th NCERT. From the Chapter 11 Area related to Circle. Give answer according to your understanding.
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