Geometry: Common Core (15th Edition)

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

Chapter 8 - Right Triangles and Trigonometry - Get Ready! - Page 487: 8

Answer

$x = 12$

Work Step by Step

The altitude of a right triangle is the geometric mean of the lengths of the two hypotenuse segments. Let's set up that proportion: The geometric mean of two numbers can be found using the following proportion: $\frac{a}{x} = \frac{x}{b}$, where $a$ and $b$ are the lengths of the two hypotenuse segments, and $x$ is the length of the altitude. Let's plug in our numbers: $\frac{9}{x} = \frac{x}{16}$ Use the cross products property to get rid of the fractions: $x^2 = 144$ Take the positive square root to solve for $x$: $x = 12$
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