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: 37

Answer

$\approx$14.2ft

Work Step by Step

The golden ratio is $\frac{1+\sqrt{5}}{2}=\frac{length}{width}$. If the length is 23 ft, we solve for $w$, or the width. We can do this by cross multiplying. $\frac{1+\sqrt{5}}{2}=\frac{23}{w} w(1+\sqrt{5})=46, w=\frac{46}{1+\sqrt{5}}\cdot \frac{1-\sqrt{5}}{1-\sqrt{5}}=\frac{46-46\sqrt{5}}{1-5}=\frac{46-46\sqrt{5}}{-4}=\frac{23\sqrt{5}-23}{2} \approx 14.2ft$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.