Find the side of a right triangle if median is 5√3

Let’s designate the side of a regular triangle – a.
The median in a regular triangle is also the height.
Consider a right-angled triangle, in which one of the legs is 5√3, the second leg is a / 2, the hypotenuse is a.
We write down the Pythagorean theorem:
a² = (5√3) ² + (a / 2) ²
a² = 75 + a² / 4
4a² – a² = 300
3a² = 300
a² = 100
a = ± 10
In response, we take a positive root.
Answer: the side of a regular triangle is 10 units.