Question

If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?

Answer 1

Area of an equilateral triangle having each side a cm is given by 

`A = sqrt(3a^2)/a`

Now, Area of an equilateral triangle, say A₁ if each side is tripled is given by

a = 3a

`A_1 = sqrt(3)/4a^2`

`A_1 = sqrt(3)/4(3a)^2`

`A_1 = (9sqrt(3)a^2)/4  cm ^2`

Therefore, increase in area of triangle

= A₁-A 

`=(9sqrt(3a^2))/4 - sqrt(3a^2)/4`

`= (8sqrt(3a^2))/4`

Percentage increase in area

`(8sqrt(3a^2)/4)/(sqrt(3a^2)/4)  xx 100`

= 800%