Q.4 The area of an equilateral triangle is √3. What is the perimeter of the triangle?
(A) 2 (B) 4 (C) 6 (D) 8

The equilateral triangle area √3 perimeter problem challenges students to apply geometric formulas precisely. This guide breaks down the calculation, verifies options, and equips learners for competitive exams.

Step-by-Step Solution

Start with the area formula derived from base-height relationships in an equilateral triangle:

(√3/4) a² = √3

Divide both sides by √3:

(1/4) a² = 1, so a² = 4.

Take the square root: a = 2 (positive value for length).

Perimeter = 3 × 2 = 6

Option Analysis

• (A) 2: This matches one side length (a = 2), not the full perimeter.
• (B) 4: If a ≈ 1.33, area would be ≈ 0.77, too small.
• (C) 6: Correct perimeter.
• (D) 8: If a = 8/3 ≈ 2.67, area ≈ 3.09, too large.

Core Formula

The equilateral triangle area √3 perimeter relies on:

A = (√3/4) a²

Setting A = √3 yields a = 2, so the perimeter = 6.

Verification Steps

Solve (√3/4) a² = √3, simplify to a² = 4, a = 2, perimeter 3a = 6.

Cross-check: height h = (√3/2) × 2 = √3, area ½ × 2 × √3 = √3 confirms.