JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q79

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MathematicsSingle correct+4 / -1Question 79 of 90

The base of an equilateral triangle is along the line given by $3x+4y=9$ . If a vertex of the triangle is $(1,2)$ , then the length of a side of the triangle is :

\dfrac{2\sqrt3}{15}

\dfrac{4\sqrt3}{15}

\dfrac{4\sqrt3}5

\dfrac{2\sqrt3}5

Answer and worked solution

Official answer: B

The height is the distance from $(1,2)$ to the base: $h=\dfrac{|3+8-9|}5=\dfrac25$ . The side is
$\frac{2h}{\sqrt3}=\frac4{5\sqrt3}=\frac{4\sqrt3}{15}.$

Topics:Distance of a point from a line

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 79