Question

If each side of an equilateral triangle is triples then what is the percentage increase in the area of the triangle?

Answer 1

The percentage of the area of the triangle = 800%

Let the original side of the equilateral triangle be equal to a.

Initial Area of the triangle = (√3/4) a²

When the side of the triangle is tripled , new side = 3a

Final area = √3/4 (3a)²

Increase in the area of the equilateral triangle = (√3/4) (3a)² - (√3/4) a²

= (√3/4) (9a² - a²)

= (√3/4) 8a²

Percentage increase in the area of the equilateral triangle = (increase in area / initial area of the triangle) × 100

= ((√3/4) 8a²/(√3/4) a²) × 100

= 800%