Chapter 9.1, Problem 73E

To determine

To Find: The width of the text, if the text in the book shownforms a golden rectangle.

  

Answer to Problem 73E

The required width of the text is about 4 inches.

Explanation of Solution

Given information:

The text in the book shown forms a golden rectangle.

  

Calculation:

The ratio of length to the width of a golden rectangle is $\left(1+\sqrt{5}\right):2$.

The length of the text is 6 inches.

Let “w” be the width of the text.

Use the ratio $\left(1+\sqrt{5}\right):2$ to write a proportion and solve for w.

  $\frac{\left(1+\sqrt{5}\right)}{2}=\frac{6}{w}$

(Write a proportion)

  $w\left(1+\sqrt{5}\right)=12$

(Cross products property)

  $w=\frac{12}{\left(1+\sqrt{5}\right)}$

(Divide each side by $1+\sqrt{5}$ )

  $w=\frac{12}{1+\sqrt{5}}\cdot \frac{1-\sqrt{5}}{1-\sqrt{5}}$

(Multiply the numerator and denominator by the conjugate)

  $\begin{array}{l}w=\frac{12-12\sqrt{5}}{-4}\\ w=3.708\end{array}$

(Simplify)

The width of text is about 4 inches.