The median of an equilateral triangle is 13√3. Find a side of it.

The median of an equilateral triangle is 13√3

1. From the condition it is known that we are considering an equilateral triangle, so the height is both the median and the bisector.

2. We use the Pythagorean theorem: h ^ 2 = (2a) ^ 2 – a ^ 2;
h ^ 2 = 4a ^ 2 – a ^ 2;
h ^ 2 = 3a ^ 2.

3. The height is known to us, it is equal to the value of the median and is equal to 13√3. Substitute: (13√3) ^ 2 = 3a ^ 2;
507 = 3a ^ 2;
a ^ 2 = 507/3;
a ^ 2 = 169;
a = 13.

4.2a = 2 * 13 = 26 cm.

Answer: 26 cm.