The height of an equilateral triangle is 3 cm. find the side of this equilateral triangle.

In order to find the length of the side of an equilateral triangle, the median length of which is 3 cm, 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.

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 3 cm.

We apply the Pythagorean theorem and get.

x ^ 2 = (x / 2) ^ 2 + (3) ^ 2;

x ^ 2 = 9 + x2 / 4;

4x ^ 2 = 36 + x ^ 2;

4x ^ 2 – x ^ 2 = 36;

3x ^ 2 = 36;

x ^ 2 = 36: 3;

x ^ 2 = 12;

x = √12;

x = 2√3 is the length of the side of the triangle.