Problem 69.
Square Inscribed in a Triangle.
Level: High School, SAT Prep, College

In the figure below, b and h are the
base and the altitude of a triangle ABC, s is the side of the
square inscribed along the base. Prove that: \(s = \dfrac{b \cdot h}{b+h}\)
(s is one-half the harmonic mean of b and h).