Question

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

• A. $\sqrt{\frac{1}{3}}$
• B. $\sqrt{3}$
• C. $\sqrt{\frac{2}{3}}$
• D. $\sqrt{\frac{3}{2}}$

Answer 1

Answer: (C)

$\sqrt{\frac{2}{3}}$

Given

eq of base

$x+y=2$---(1)

vertex V$(2,-1)$

Now to find length of sides we calculate length of altitude as (using distance formula):

$d=\left|\frac{2-1-2}{\sqrt{1^2+1^2}}\right|$

$d=\left|\frac{-1}{\sqrt{2}}\right|$

$d=\frac{1}{\sqrt{2}}$

Now, using properties of equilateral triangle

$\frac{\sqrt{3}}{2}l=d=\frac{1}{\sqrt{2}}$

or,

$l=\sqrt{\frac{2}{3}}$