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: 26

Answer

The triangle is not a right triangle.

Work Step by Step

RECALL: If the sides of a triangle satisfies $c^2=a^2+b^2$ (from the Pythagorean Theorem) where c is the hypotenuse (the longest side) and a and b are the two other sides, then the triangle is a right triangle. Substitute the given side-lengths to obtain: $c^2=a^2+b^2 \\7^2=4^2+5^2 \\49=16+25 \\49\ne41$ The triangle's side lengths do not satisfy the equation, so the triangle is NOT a right triangle.
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