Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises - Page 178: 57

Answer

$$\color{blue}{x=0.5\text{ft}}$$

Work Step by Step

$(\text{area of the outer rectangle})-(\text{area of the inner rectangle}=21)$ $12(10)-(12-2x)(10-2x)=21$ $120-(120-24x-20x+4x^2)=21$ $120-120+44x-4x^2=21$ $4x^2+44x=21$ $4x^2+44x-21=0$ Use the quadratic formula: $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ $x=\dfrac{-(44)\pm\sqrt{(44)^2-4(-4)(-21)}}{2(-4)}$ $x=\dfrac{-44\pm\sqrt{1600}}{-8}$ $x=\dfrac{-44+40}{-8}$ or $x=\dfrac{-44-40}{-8}$ $x=\dfrac{-4}{-8}$ or $x=\dfrac{-84}{-8}$ $x=0.5$ or $x=10.5$ Since 10.5ft is larger than the wall we know that: $\color{blue}{x=0.5\text{ft}}$
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