Acute-angled triangle ABC. BM median, BH height. If MH = 10cm then find the length AC.

1. AM = CM, since ВM, according to the problem statement, is the median and divides the side of the triangle to which it is drawn into two identical segments.

2. Triangle AСН is rectangular, since СН, according to the problem statement, is height.

3. In the indicated triangle НM is the median, since it divides AC into two identical segments AM and CM.

4. AC in this triangle is the hypotenuse.

5. According to the theorem, the median drawn from a right angle to the hypotenuse is equal to its half.

That is, AC = MH x 2 = 10 x 2 = 20 centimeters.

Answer: The length of the speaker is 20 centimeters.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.