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 - 8-1 The Pythagorean Theorem and It's Converse - Lesson Check - Page 495: 2

Answer

$\sqrt {130}=x$

Work Step by Step

The Pythagorean Theorem states that if $a$ and $b$ are the legs of a right triangle and $c$ is the hypotenuse, then $a^2+b^2=c^2$. We plug in the values for $a$, $b$, and $c$, using the legs and the hypotenuse of the right triangle shown, and then solve the equation using the properties of algebra and equality: $$7^2+9^2=x^2$$$$49+81=x^2$$$$130=x^2$$$$\sqrt {130}=\sqrt {x^2}$$$$\sqrt {130}=x$$
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