The area of an equilateral triangle increases by 16√3

Solution

Let length of each side of the equilateral triangle = ‘x’ units After increment, length of each side of the equilateral triangle = (x + 4) units According to the question, (√3/4) × (x + 4)² – (√3/4) × x² = 16√3 Or, (√3/4) × [(x + 4)² – x²)] = 16√3 Or, (1/4) × [x² + 16 + 8x – x²)] = 16 Or, (1/4) × (16 + 8x) = 16 Or, 16 + 8x = 64 Or, 8x = 48 Or, x = 6 Therefore, original perimeter of the equilateral triangle = 3x = 6 × 3 = 18 units