Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.5 Applications and Modeling with Quadratic Equations - 1.5 Exercises: 3

Answer

$x^{2}+(2x-2)^{2}$ $=$ $(x+4)^{2}$

Work Step by Step

In the given triangle, $(x+4)$ is the hypotenuse whereas $x$ and $(2x-2)$ form the arms of the triangle. According to the Pythagoras theorem, $ {a^{2}+b^{2}}$ $=$ $c^{2}$ Where a and b are arms of triangle and c is the hypotenuse. Substituting the values in the above formula we get, $x^{2}+(2x-2)^{2}$ $=$ $(x+4)^{2}$ Hence, the answer is option D.
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