Question : If the area of an equilateral triangle is $a$ and height $b$, then the value of $\frac{b^2}{a}$ is:
Option 1: $3$
Option 2: $\frac{1}{3}$
Option 3: $\sqrt3$
Option 4: $\frac{1}{\sqrt3}$
Correct Answer: $\sqrt3$
Solution :
The Area of the equilateral triangle = $\frac12×\ \text{base × height}$
$⇒a= \frac12×\ \text{base}\ ×b$
$\therefore$ base $= \frac{2a}{b}$
Now,
Area of an equilateral triangle $= \frac{\sqrt3}{4}\times (\text{side})^2$
$⇒a= \frac{\sqrt3}{4}\times (\frac{2a}{b})^2$
$⇒\frac{b^2}{a} = \sqrt3$
Hence, the correct answer is $\sqrt3$.
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