Chapter 7.3, Problem 1E

To determine

To measure: the appropriate lengths to the nearest millimeter and compute the ratios with a calculator.

Answer to Problem 1E

  $\begin{array}{l}\frac{AD}{AC}=1.613\\ \frac{AC}{AB}=1.632\\ \frac{AB}{BC}=1.583\end{array}$

Explanation of Solution

Given Information:

A regular pentagon is shown. It happens to be true that $\frac{AD}{AC},\frac{AC}{AB},$ and $\frac{AB}{BC}$ all equal the golden ratio.

Given figure,

  

Calculation:

The required measurements are:

  $\begin{array}{l}AD=10cm\\ AC=6.2cm\\ AB=3.8cm\\ BC=2.4cm\end{array}$

Now the ratio $\frac{AD}{AC}$ is computed as,

  $\frac{AD}{AC}=\frac{10}{2}=1.613$

Hence, the ratio $\frac{AD}{AC}=1.613$ .

Now the ratio $\frac{AC}{AB}=\frac{6.2}{3.8}=1.632$

Hence, the ratio $\frac{AC}{AB}=1.632$

Now, the ratio $\frac{AB}{BC}$ is computed as,

  $\frac{AB}{BC}=\frac{3.8}{2.4}=\frac{38}{24}=1.583$

Hence, the ratio $\frac{AB}{BC}=1.583$ .