Find the side length of an equilateral triangle if its median is 5√3 dm.

In an equilateral triangle, the median drawn to either side is also the height. This means that the triangle formed by the side, the median and half of the side to which the median is drawn is rectangular. Therefore, by the Pythagorean theorem, we can write:

a ^ 2 + (a / 2) ^ 2 = m ^ 2;

a ^ 2 + a ^ 2/4 = m ^ 2;

5a ^ 2/4 = (5√3) ^ 2;

5a ^ 2 = 4 * 25 * 3 = 300;

a ^ 2 = 300/5 = 60;

a = √60 = 2√15 dm – the side of this equilateral triangle.