Triangle ABD, DM is perpendicular to AB, AB = 14, AD = 15, BD = 13. Find the height of the triangle.

1. According to the problem statement, DM is perpendicular to AB. Therefore, triangles BMD and AMD are rectangular.

2. We take the length of the ВM segment as x. Hence, AM = AB – x = 14 – x.

3. DМ² = ВD² – ВМ² = 13² – х² = (169 – х²) (according to the Pythagorean theorem from the triangle ВDM).

4. DМ² = АD² + АМ² = 15² – (14 – x) ² = 225 – 196 + 28x – x² (according to the Pythagorean theorem from the triangle АМD).

169 – x² = 225 – 196 + 28x – x²;

28x = 140;

x = 5.

ВM = 5 units of measurement.

5. We calculate the length of the height DМ:

DМ = √ВD² – ВМ² = √13² -5² = √169 – 25 = √144 = 12 units.

Answer: the height DМ is equal to 12 units of measurement.