The bisector of an equilateral triangle is 12√3. find his side.

The solution of the problem:

1) To begin with, remember that in an equilateral triangle, all angles are equal to 60 degrees.

Let the bisector be AH and the desired side AB.

The ВAН angle is 30 degrees, because AH divides angle A in half.

2) In an equilateral triangle, the bisector is the median and the height, therefore, the triangle АНВ is right-angled.

In a right-angled triangle opposite an angle of 30 degrees lies a leg equal to half of the hypotenuse.

So AB = 1/2 AH

AB = 12√3 / 2

AB = 6√3.

Answer: the side of an equilateral triangle is 6√3.