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

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9.Straight Line

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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

$\sqrt {\frac{{20}}{3}} $

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

$\sqrt {\frac{8}{{15}}} $

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

Solution

(a) $AD = \left| {\,\frac{{ – 2 – 2 – 1}}{{\sqrt {{{(2)}^2} + {{( – 1)}^2}} }}\,} \right| = \left| {\,\frac{{ – 5}}{{\sqrt 5 }}\,} \right| = \sqrt 5 $

$\tan {60^o}$ $ = \frac{{AD}}{{BD}} \Rightarrow \sqrt 3 = \frac{{\sqrt 5 }}{{BD}}$==> $BD = \sqrt {\frac{5}{3}} $

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

Standard 11

Mathematics

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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

Solution

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