The orthocenter of a right-angled triangle is formed

$\mathrm{ABC}$ is an equilateral triangle of side $2\mathrm{a}$, then length of one of its altitude is $a\sqrt{x}$. The value of $\mathrm{a}$ is _____.

Which of the following figures will have it's altitude outside the triangle?

Draw all three altitudes for the following triangles and explain how they are different:

If $CF\perp ED$, name the altitude of $\mathrm{\Delta }\mathrm{E}\mathrm{C}\mathrm{D}.$

Write the definition of the altitude of a triangle.

If $\mathrm{\Delta }\mathrm{E}\mathrm{B}\mathrm{D}$ is a right triangle, name the two altitudes of $△\mathrm{EBD}$.