Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises: 36

Answer

$ \approx 4.9$ inches

Work Step by Step

In the Golden Rectangle Ratio, length to width: $(1+\sqrt{5}):2$. Length is 8, and let $w$ be the width. We set up the following equation: $\frac{w}{8}=\frac{2}{1+\sqrt{5}}$. $w=\frac{16}{1+\sqrt{5}}$ We now multiply both sides by the conjugate of the denominator.$\frac{16}{1+\sqrt{5}}\cdot \frac{1-\sqrt{5}}{1-\sqrt{5}}=\frac{16(1-\sqrt{5})}{1-5}=\frac{16(1-\sqrt{5})}{-4}=4(\sqrt{5}-1) \approx 4.9$ inches
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