Triangle ABC, BH-height AB = 15 cm, BC = 20cm, AC = 25, BH-?

In triangle ABC, the height BH is drawn, which divided ABC into two triangles. These triangles are rectangular because the property of height is that it forms a right angle with the side to which it is drawn.
Let us denote by x the side of AH, and the side of the HC will then be equal to 25 – x.
Let us express the height BH using the Pythagorean theorem in different ways, and then equate them and the mode equation:
BH² = 15² – x²;
BH² = 225 – x²;
BH = √ (225 – x²);
BH² + (25 – x) ² = 20²;
BH = √ (400 – 625 + 50x – x²);
225 – x² = 400 – 625 + 50x – x²;
50x = 450;
x = 9 (cm).
BH² = 225 – 81;
BH = 12 (cm).
ANSWER: BH = 12 cm.