The median of an equilateral triangle is 11√3 Find the side of this triangle.

In order to find the length of the side of an equilateral triangle, the median length of which is 11√3, let’s reason. By the property of an equilateral triangle, the median divides the side to which it is drawn into two equal segments. And at the same time it is height. As a result, we get two identical right-angled triangles.

We introduce the variable x, denoting the side of the triangle by it.

In a right-angled triangle, the hypotenuse will be x, one of the legs is x / 2 (half of the side to which the median is drawn), the second leg is the median equal to 11√3.

We apply the Pythagorean theorem and get.

x² = (x / 2) ² + (11√3)²;

x² = 363 + x² / 4;

4x² = 1452 + x²;

4x² – x2 = 1452;

3x² = 1452;

x² = 1452: 3;

x² = 484;

x = √484;

x = 22 side length of the triangle.