Question

lesson practice 7.1.08 name: problems 1 - 2: a book measures 6 inches wide and 9 inches tall. the publisher wants to display an image of the book on a billboard. the width of the book on the billboard is 36 inches. 1. how tall is the book on the billboard? 2. what scale is used for the image on the billboard? show or explain your thinking.

Explanation:

Step1: Set up proportion for height

The book's actual width - height ratio is the same as the bill - board's width - height ratio. Let the height of the book on the billboard be $h$. The actual width of the book is $w_1 = 6$ inches and actual height is $h_1=9$ inches, and the width on the billboard is $w_2 = 36$ inches. So, $\frac{w_1}{h_1}=\frac{w_2}{h}$.

Step2: Solve for height $h$

Substitute the values into the proportion: $\frac{6}{9}=\frac{36}{h}$. Cross - multiply gives $6h=36\times9$. Then $h=\frac{36\times9}{6}=54$ inches.

Step3: Find the scale

The scale is the ratio of the billboard dimension to the actual dimension. For the width, the scale factor $s=\frac{36}{6} = 6$. This means that the dimensions on the billboard are 6 times the actual dimensions of the book.

Answer:

1. 54 inches
2. The scale is 6:1. The width of the book is 6 inches and on the billboard it is 36 inches. Since $\frac{36}{6}=6$, each dimension on the billboard is 6 times the actual dimension of the book.