Question

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

• A. $200\%$
• B. $400\%$
• C. $600\%$
• D. $800\%$

Answer 1

Answer: (D)

$800\%$

Let the initial side be $a$ units

Area $=\sqrt{3}\frac{a^2}{4}$sq. units

Now, side is tripled

New side, $a^{\prime }=3a$

New area $=\sqrt{3}\frac{(3a{)}^2}{4}$

$=9\times \sqrt{3}\frac{a^2}{4}$

$=9\times$(initial area)

Increase in area $=9\times$ initial area - initial area $=8\times$ initial area

$\%\text{increase}=\frac{\text{increase}}{\text{initial area}}\times 100$

$=\frac{8\times \text{initial area}}{\text{initial area}}\times 100$

$=800$ %