College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.3 - Geometry Essentials - R.3 Assess Your Understanding - Page 36: 21

Answer

The triangle is not a right triangle.

Work Step by Step

A right triangle has three sides that satisfy the equation $c^2=a^2+b^2$ where $c$ is the longest side (hypotenuse) and $a$ and $b$ are the two other sides. Substitute the given lengths of sides to the equation above to obtain: $c^2=a^2+b^2 \\6^2=4^2+5^2 \\36=16+25 \\36\ne 41$ The triangle's side lengths do not satisfy the equation; therefore the triangle is NOT a right triangle.
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