Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 9 - Solving Quadratic Equations - 9.1 - Properties of Radicals - Exercises - Page 487: 73

Answer

$w\approx 3.7$ in

Work Step by Step

Ratio of the length to the width in Golden rectangle is $\frac{1+\sqrt5}{2}$. So: $$\frac{1+\sqrt5}{2}=\frac{6}{w}$$ $$w(1+\sqrt5)=12$$ $$w=\frac{12}{1+\sqrt5}$$ $$w=\frac{12(1-\sqrt5)}{(1+\sqrt5)(1-\sqrt5)}=\frac{12(1-\sqrt5)}{1-5}\approx3.7$$
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