Chapter 6.5, Problem 13E

To determine

To calculate: Length and perimeter of the poster.

Answer to Problem 13E

Length of the poster = $3.75\text{ feet}$

Perimeter of the poster = $12.5\text{ feet }$

Explanation of Solution

Given information:

Length of photograph = $6$ inches

Width of photograph = $4$ inches

Width of poster = $2.5$ feet

The poster will be similar to the original photograph.

Calculation:

To find the length of the poster, use the ratio of the side lengths of the corresponding sides of the photograph and poster. Since the photo and the poster are similar, the ratio of corresponding sides will be equal. To find perimeter, add all the sides of the poster. Write

  $2.5\text{ feet}=2.5\times 12=30\text{ inches}$ . Let length of the poster be $x$ inches

Ratio of the corresponding side length=

  $\begin{array}{l}\frac{\text{Length of poster}}{\text{Length of photo}}=\frac{\text{Width of poster}}{\text{Width of photo}}\text{ [Write proportion]}\\ \frac{x}{6}=\frac{30}{4}\text{ [Substitute values]}\\ x\cdot 4=30\cdot 6\text{ [Form cross product]}\\ \text{ 4}x=180\text{ [Multiply]}\\ x=45\text{ [Divide each side by 45]}\end{array}$

Therefore, length of the poster = $45\text{ inches}=\frac{45}{12}=3.75\text{ feet}$

Perimeter of the poster

  $\begin{array}{l}\text{=2(length}+\text{breadth)}\\ =2(2.5+3.75)\text{ [Substitute]}\\ =2\cdot 6.25\text{ [Add]}\\ =12.5\text{ feet [Multiply]}\end{array}$