Question
The area of an equilateral triangle increases by 16√3
square units when the length of each side is increased by 4 units. What is the original perimeter of the triangle?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
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