The geometric mean of two numbers a and b is, by definition, square root(ab). Prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments into which the altitude partitions the hypotenuse.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.1: Rectangular Coordinate Systems
Problem 36E
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The geometric mean of two numbers a and b is, by definition, square root(ab). Prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments into which the altitude partitions the hypotenuse.

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