Question 207293
Dropping the altitude, creates 2 right triangles. Each triangle has a hypotenuse of length a, a shorter side with length a/2 and the altitude h.
Using Pythagorean theorem
{{{a^2 = (a/2)^2 + h^2}}}
{{{a^2 - a^2/4 = h^2}}}
{{{(3a^2)/4 = h^2}}}
{{{sqrt(3a^2/4) = h}}}
{{{sqrt(3)*a/2 = h}}}