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 - Page 130: 26

Answer

$1\ ft$

Work Step by Step

Step 1. Assume the width of the border is $x$, the size of the center rectangle would be $9-2x$ by $5-2x$ Step 2. The area of the center rectangle would be $A_1=(9-2x)(5-2x)$ Step 3. The total area is $A=9\times5=45$ and the area of the border would be $A_2=A-A_1=45-(9-2x)(5-2x)=18x+10x-4x^2=28x-4x^2$ Step 4. Let $A_2=24$, we have $28x-4x^2=24$ or $x^2-7x+6=0$ which gives $x=1\ or\ 6$ Step 5. Discard $x=6$ as it is not practical. Thus $x=1\ ft$
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