Vertex of an equilateral triangle is (2,-1) and equation of its base in x + 2y = 1 . length of its s

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9.Straight Line

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

A

$4/\sqrt {15} $

B

$2/\sqrt {15} $

C

$4/3\sqrt 3 $

D

$1/\sqrt 5 $

Solution

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

$\tan 60^\circ = \frac{{AD}}{{BD}}$

==> $\sqrt 3 = \frac{{1\,/\sqrt 5 }}{{BD}}$

==> $BD = \frac{1}{{\sqrt {15} }}$

$BC = 2BD = 2\,/\sqrt {15} $.

Standard 11

Mathematics

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