Chapter 7.3, Problem 2E

To determine

To Express: $\frac{l}{w}$ in golden ratio such that $\frac{l}{w}=\frac{l+w}{l}=\frac{1+\sqrt{5}}{2}$ .

Answer to Problem 2E

  $1.618$

Explanation of Solution

Given:

  $\frac{l}{w}=\frac{l+w}{l}=\frac{1+\sqrt{5}}{2}$

Calculation:

Since, golden ratio is the special number approximately equal to $1.618$ .

Here, it expressed as.

  $\begin{array}{l}\frac{l}{w}=\frac{1+\sqrt{5}}{2}\\ \frac{l}{w}=\frac{1}{2}+\frac{\sqrt{5}}{2}\\ \frac{l}{w}=0.5+1.118\\ \frac{l}{w}=1.618\\ or\\ \frac{l}{w}=1+\frac{1}{1.618}\end{array}$

Therefore, the answer is $1.618$ .