If the base of an Isosceles triangle is 2a and the length of the altitude dropped to the base is h then the distance from the midpoint of the base to side of triangle is

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$\frac{ah}{\sqrt{a^{2} + h^{2}}}$

$\frac{ah}{\sqrt{a^{2} - h^{2}}}$

$\frac{ah}{\sqrt{h^{2} - a^{2}}}$

$\sqrt{a^{2} + h^{2}}$

answer is A.

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Detailed Solution

Consider the equilateral triangle, having base along x-axis with vertices $A (- a, 0), B (a, 0)$ and third vertex $C (0, h)$
This is the triangle having the base of an Isosceles triangle is 2a and the length of the altitude dropped to the base is h
The midpoint of the base is origin.
The equation of one side is the equation of the line joining the points $B (a, 0)$ and $C (0, h)$
Equation of side is $\frac{x}{a} + \frac{y}{h} = 1 \Rightarrow hx + ay = ah$
The distance from origin to the above line is $\frac{ah}{\sqrt{h^{2} + a^{2}}}$