Chapter 11.8, Problem 11IP

To determine

To find: What are the dimensions of the largest Iron-on.

Answer to Problem 11IP

Dimensions of the photo for the cover on the scrap book is $6.75$ inches and $11.25$ inches.

Yes, all three photos are similar since each enlargement was the result of a dilation.

Explanation of Solution

Given information:

The Original dimensions of the photo is

  $L_1=3$ inches.

  $W_1=5$ inch.

First Scale factor for iron on at the back $=k_1=1.5$ to place in the scrap book

Second Scale factor for iron on for the front $=k_2=1.5$ to place on the cover on the scrap book

Given

The Original dimensions of the photo is

  $L_1=3$ inches.

  $W_1=5$ inches.

Let $L_2$ inch and $W_2$ inch be the dimensions of the second photo to place in the scrap book.

  $\begin{array}{l}{L}_2=L_1\times k_1\\ \Rightarrow L_2=3\times 1.5\\ \Rightarrow L_2=4.5\end{array}$

  $\begin{array}{l}{W}_2=W_1\times k_1\\ \Rightarrow W_2=5\times 1.5\\ \Rightarrow W_2=7.5\end{array}$

Therefore,

Dimensions of the second photo to place in the scrap book is $4.5$ inchesby $7.5$ inches.

Now,

The second photo is enlarged by a scale factor of $1.5$ to place on the cover on the scrap book.

Let $L_3$ inch and $W_3$ inch be the dimensions of the photo for the cover on the scrap book

  $\begin{array}{l}{L}_3=L_2\times k_2\\ \Rightarrow L_3=4.5\times 1.5\\ \Rightarrow L_3=6.75\end{array}$

  $\begin{array}{l}{W}_3=W_2\times k_2\\ \Rightarrow W_3=7.5\times 1.5\\ \Rightarrow W_3=11.25\end{array}$

Therefore,

Dimensions of the photo for the cover on the scrap book is $6.75$ inches and $11.25$ inches.

Yes, all three photos are similar since each enlargement was the result of a dilation.