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Q.
If the equation of base of an equilateral triangle is $2x - y = 1$ and the vertex is $(- 1, 2)$, then the length of the side of the triangle is
Straight Lines
Solution:
$\Delta ABC$ is an equilateral triangle. $AD$ is altitude.Equation of $BC$ is $2x - y = 1$
So perpendicular distance,
$AD=\left|\frac{2\left(-1\right)-2-1}{\sqrt{4+1}}\right|$
$=\left|-\sqrt{5}\right|=\sqrt{5}$
In $\Delta ABD$, $\frac{AD}{AB}=sin\,60^{\circ}$
$\Rightarrow \frac{\sqrt{5}}{AB}=\frac{\sqrt{3}}{2}$
$\therefore AB=\frac{2\sqrt{5}}{\sqrt{3}}=\sqrt{\frac{20}{3}}$ units
