A book measures `6` in. wide and `9` in. tall. The publisher wants to display an image of the book on a billboard. The width of the book on the billboard is `36` in.How tall is the book on the billboard

The dimensions of the book are 6 inches wide and 9 inches tall. To maintain the aspect ratio when enlarging the book's width to 36 inches, we use the following proportion:

\[
\frac{\text{original width}}{\text{original height}} = \frac{\text{billboard width}}{\text{billboard height}}
\]

Substituting the known values:

\[
\frac{6}{9} = \frac{36}{\text{billboard height}}
\]

To find the billboard height, solve for it by cross-multiplying:

\[
6 \times \text{billboard height} = 36 \times 9
\]

\[
6 \times \text{billboard height} = 324
\]

\[
\text{billboard height} = \frac{324}{6} = 54 \, \text{inches}
\]

Thus, the height of the book on the billboard is **54 inches**.

Would you like further details or clarifications?

Here are 5 related questions for practice:
1. If the book's width was increased to 48 inches, what would be the new height?
2. How would you calculate the area of the image of the book on the billboard?
3. If the publisher wanted the image to be 72 inches tall, what would be the width?
4. How would the aspect ratio change if the height of the billboard image was not proportional to the width?
5. What would the scale factor be for converting the book’s original size to the billboard size?

**Tip:** Keeping the aspect ratio consistent ensures that the image does not appear stretched or distorted.

A book measures 6 in. wide and 9 in. tall. The publisher wants to display an image of the book on a billboard. The width of the book on the billboard is 36 in. How tall is the book on the billboard?

Learn how to solve a proportions problem where the dimensions of a book are scaled up for display on a billboard. The problem involves maintaining the aspect ratio between the original book and the enlarged billboard image. Suitable for Grades 6-8 students.

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