First slide

Equation of line in Straight lines

Question

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

Moderate

A

$\sqrt{20 / 3}$
B

$2 / \sqrt{15}$
C

$\sqrt{8 / 15}$
D

$\sqrt{15 / 2}$

Solution

$AD = |\frac{- 2 - 2 - 1}{\sqrt{{(2)}^{2} + {(- 1)}^{2}}}| = |\frac{- 5}{\sqrt{5}}| = \sqrt{5}$
$∵ \tan 60^{0} = \frac{AD}{BD}$
or $\sqrt{3} = \frac{\sqrt{5}}{BD}$
or $BD = \sqrt{\frac{5}{3}}$
$∴ BC = 2 BD = 2 \sqrt{\frac{5}{3}} = \sqrt{\frac{20}{3}}$

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