Point H is the base of the height drawn from the apex of the right angle B of triangle ABC

Point H is the base of the height drawn from the apex of the right angle B of triangle ABC to hepotinuse AC. Find AB if AH = 5 AC = 45.

ВН – the height of the triangle ABC (by condition).
Consider right-angled triangles ABН and ABC, they are similar (acute angle A – common).
From the similarity of triangles, we write down the ratio of linear measurements:
AB / AC = AH / AB
AB² = AC * AH
AB = √ (45 * 5) = √225 = 15.
Answer: the length of AB is equal to 15 linear units.