Find the height of an equilateral triangle if its side is 6 cm.

Equilateral is a triangle in which all three sides are equal:

AB = BC = AC = 6 cm.

In an equilateral triangle, the height drawn to the side divides it into two equal segments:

AH = AC = AC / 2;

AH = AC = 6/2 = 3 cm.

To calculate the height BH, consider the triangle ΔABH. This triangle is rectangular.

We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BH ^ 2 + AH ^ 2;

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 6 ^ 2 – 3 ^ 2 = 36 – 9 = 25;

BH = √25 = 5 cm.

Answer: The length of the HV height is 5 cm.