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  4. An equilateral triangle is inscribed in the parabola y2=8 x, with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle is

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Q. An equilateral triangle is inscribed in the parabola $y^{2}=8 \,x$, with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle is

AP EAMCETAP EAMCET 2015

Solution:

Let $l$ be the length of an equilateral triangle.
image
Then, from above figure, we can say that $\left(\frac{\sqrt{3}}{2} l, \frac{l}{2}\right)$
will lie on parabola $y^{2}=8 x$.
$\Rightarrow \left(\frac{l}{2}\right)^{2}=8\left(\frac{\sqrt{3}}{2} l\right) \Rightarrow l^{2}=16 \sqrt{3} l \Rightarrow l=16 \sqrt{3}$ units