Question

The vertex of an equilateral triangle is (2, –1) and the equation of its base is $x + 2 y = 1$. The length of its sides is

• A. $\frac { 4 } { \sqrt { 15 } }$
• B. $\frac { 2 } { \sqrt { 15 } }$
• C. $\frac { 4 } { 3 \sqrt { 3 } }$
• D. None of these

Answer 1

Answer: (B)

$\frac { 2 } { \sqrt { 15 } }$

Answer 2

$| A D | = \left| \frac { 2 - 2 - 1 } { \sqrt { 1 ^ { 2 } + 2 ^ { 2 } } } \right| = \frac { 1 } { \sqrt { 5 } }$

$B D = \frac { 1 } { \sqrt { 15 } }$

⇒ $B C = 2 B D = \frac { 2 } { \sqrt { 15 } }$