Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - 7-4 Similarity in Right Triangles - Practice and Problem-Solving Exercises - Page 465: 12


$2 \sqrt {10}$

Work Step by Step

The geometric mean of two numbers can be found using the following proportion: $\frac{a}{x} = \frac{x}{b}$, where $a$ and $b$ are positive numbers and $x$ is the geometric mean. Let's plug in our numbers: $\frac{4}{x} = \frac{x}{10}$ Use the cross products property to get rid of the fractions: $x^2 = 40$ Rewrite $40$ as the product of a perfect square and another factor: $x^2 = 4 • 10$ Take the positive square root of each factor to solve for $x$: $x = 2 \sqrt {10}$
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