Prove that in a triangle the length of any altitude is smaller than the sides that are meeting at the altitude's vertex.

Question

Prove that in a triangle the length of any altitude is smaller than the sides that are meeting at the altitude's vertex.

Answer 1

An informal proof:

Each of the 2 sides meeting at the vertex is the hypotenuse of a right triangle of which the altitude is a leg...and each leg of a right triangle is shorter than the hypotenuse.