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  • Can someone help me with this, 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 :

 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 :

  • Option 1)

    \frac{2\sqrt{3}}{15}

  • Option 2)

    \frac{4\sqrt{3}}{15}

  • Option 3)

    \frac{4\sqrt{3}}{5}

  • Option 4)

    \frac{2\sqrt{3}}{5}

 

Answers (1)

best_answer

As we learnt in

Perpendicular distance of a point from a line -

\rho =\frac{\left | ax_{1}+by_{1}+c\right |}{\sqrt{a^{2}+b^{2}}}

 

 

- wherein

\rho  is the distance from the line ax+by+c=0 .

AD=P=\frac{3(1)+4(2)-9}{\sqrt{3^{2}+4^{2}}}=\frac{2}{5}

Also h=\frac{\sqrt{3}}{2}\:a\:=\:\frac{2}{5}

Thus a=\frac{4\sqrt{3}}{15}


Option 1)

\frac{2\sqrt{3}}{15}

This option is incorrect.

Option 2)

\frac{4\sqrt{3}}{15}

This option is correct.

Option 3)

\frac{4\sqrt{3}}{5}

This option is incorrect.

Option 4)

\frac{2\sqrt{3}}{5}

This option is incorrect.

Posted by

divya.saini

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