Question

The equation of the base of an equilateral triangle ABC is

x + y = 2 and the vertex is (2, –1). The area of the triangle ABC is

• A. $\frac { \sqrt { 2 } } { 6 }$
• B. $\frac { \sqrt { 3 } } { 6 }$
• C. $\frac { \sqrt { 3 } } { 8 }$
• D. None

Answer 1

Answer: (B)

$\frac { \sqrt { 3 } } { 6 }$

Answer 2

Let side AB is x

\ length AD = $\frac { | 2 - 1 - 2 | } { \sqrt { 2 } }$= $\frac { 1 } { \sqrt { 2 } }$

In DABD, sin 60⁰ =

$\frac { \sqrt { 3 } } { 2 } = \frac { 1 } { \sqrt { 2 } x }$ Ž x = $\frac { \sqrt { 2 } } { \sqrt { 3 } }$

\ area of equilateral D = $\frac { \sqrt { 3 } } { 4 } \frac { 2 } { 6 } = \frac { \sqrt { 3 } } { 6 }$

$x + y = 2$