Question

There is apoint inside an equilateral triangle which is at distances1,2 and 3 from the three sides The area of the triangle is

• A. not uniquely determinable
• B. 6
• C. $6\sqrt{3}$
• D. $12\sqrt{3}$

Answer 1

The correct option is D $12\sqrt{3}$

Area $=\frac{1}{2}[x+2x+3x]=\frac{\sqrt{3}{x}^2}{4}$
$\Rightarrow 3x=\frac{\sqrt{3}{x}^2}{4}$
$\Rightarrow x=4\sqrt{3}$
$\Rightarrow$ Area $=12\sqrt{1}3$