Chapter 7.1, Problem 44E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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Note: Exercises preceded by an asterisk are of a more challenging nature.

*In Exercises 39 and 42, refer to the line segments shown.*

Use the following theorem to construct the geometric mean of the numerical lengths of the segments

*Theorem:* The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.

To determine

**To construct:**

The geometric mean of the numerical lengths of the segments

Explanation

**Theorem:**

Geometric mean theorem:

The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.

**Calculation:**

Consider a right angle triangle

Consider the right triangles

Consider the right triangles

Consider the right triangles

From the above, we find that the length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse

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