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 - Practice and Problem-Solving Exercises - Page 496: 25


No $24^{2}$+$8^{2}$$\ne$$25^{2}$

Work Step by Step

The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. If this is true, then a triangle is a right triangle. This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$ You are given the lengths of the legs as 24 and 8. You are given the length of the hypotenuse as 25. Substitute 24 in for a, 8 in for b, and 25 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $24^{2}$+$8^{2}$=$25^{2}$ 576+64=625 640$\ne$725
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