Question

If the equation of base of an equilateral triangle is 2x - y = 1 and one vertex is (-1, 2), then the length of the side of the triangle is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$AD=\left|\frac{-2-2-1}{\sqrt{(2{)}^2+(1{)}^2}}\right|=\left|\frac{-5}{\sqrt{5}}\right|=\sqrt{5}\because tan{60}^{\circ }=\frac{AD}{BD}\Rightarrow \sqrt{3}=\frac{\sqrt{5}}{BD}=\sqrt{\frac{5}{3}}$

$\therefore BC=2BD=2\sqrt{\frac{5}{3}}=\sqrt{\frac{20}{3}}$