Question

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

Answer 1

Let the sides of the original triangle be a units
$\text{Area of an equilateral triangle}\left(\Delta \right)=\frac{\sqrt{3}}{4}(\text{side}{)}^2$
$=\frac{\sqrt{3}}{4}{a}^{2}sq.unnits$
Now, when side is tripled, then
New side$\left(a^{\prime }\right)=3a$
$\text{Area of new triangle}\left({\Delta }^{\prime }\right)=\frac{\sqrt{3}}{4}(a^{\prime }{)}^2$
$=\frac{\sqrt{3}}{4}\times (3a{)}^2$
$=9\times \frac{\sqrt{3}}{4}{a}^2$
$=9\Delta$
$\text{Increase in area}=9\Delta -\Delta =8\Delta$
$\%\text{Increase}=\frac{\text{increase in area}}{\text{initial area}}\times 100$
$=\frac{8\Delta }{\Delta }\times 100$
$=800\%$