Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Review - Modeling with Functions - Problems - Page 243: 24

Answer

(a) $A=(\frac{x}{4})^2+(\frac{10-x}{4})^2$ (b) $x=5cm$

Work Step by Step

(a) The side length of the first square is $\frac{x}{4}$ and its area is $(\frac{x}{4})^2$. The side length of the second square is $\frac{10-x}{4}$ and its area is $(\frac{10-x}{4})^2$. The total area would be $A=(\frac{x}{4})^2+(\frac{10-x}{4})^2$ (b) As shown in the graph, the minimum of the area happens when $x=5cm$ with $A=3.125cm^2$
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