Question : If the side of an equilateral triangle is increased by 34%, then by what percentage will its area increase?
Option 1: 70.65%
Option 2: 79.56%
Option 3: 68.25%
Option 4: 75.15%
Correct Answer: 79.56%
Solution :
Let the side of the equilateral triangle be $a$.
Area of an equilateral triangle with side $a = (\frac{\sqrt{3}}{4})a^{2}$
Side increased by 34%
So, new side $= a\times(\frac{134}{100})$
$= \frac{67a}{50}$
Area of an equilateral triangle with a new side
$=(\frac{\sqrt{3}}{4})(\frac{67a}{50})^{2}$
$= \frac{4489\sqrt{3}a^{2}}{10000}$
Change in area
$= \frac{4489\sqrt{3}a^{2}}{10000} - \frac{\sqrt{3}a^{2}}{4}$
$= \frac{1989\sqrt{3}a^{2}}{10000}$
Percentage increase
$= \frac{\frac{1989\sqrt{3}a^{2}}{10000}}{\frac{\sqrt{3}a^{2}}{4}}\times100$%
= 79.56%
Hence the correct answer is 79.56%.
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