Question

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

Answer 1

When each side of triangle = a

Area of an equilateral triangle = \(\frac{\sqrt3a^2}{4}\) = A

 A When each side of triangle = 3a

Area of an equilateral triangle = \(\frac{\sqrt3(3a)^2}{4}\)= 9 \((\frac{\sqrt3a^2}{4})\)= 9A 

Increase in area = 9A-A = 8A

Percentage increase in area = \(\frac{increase\,area}{original\,area}\times100\) = \(\frac{8A}{A}\times100\) = 800\(\text%\)