Chapter 11.8, Problem 4GP

To determine

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

Answer to Problem 4GP

Dimensions of the iron on at the front of the t-shirt is $12$ inch and $6$ inch.

Explanation of Solution

Given information:

The Original dimensions of the t-shirt iron on is

  $L_1=2$ inch.

  $W_1=1$ inch.

First Scale factor for iron on at the back $=k_1=3$

Second Scale factor for iron on for the front $=k_2=2$

Given

The Original dimensions of the t-shirt iron on is

  $L_1=2$ inch.

  $W_1=1$ inch.

Let $L_2$ inch and $W_2$ inch be the dimensions of the iron on at the back.

  $\begin{array}{l}{L}_2=L_1\times k_1\\ \Rightarrow L_2=2\times 3\\ \Rightarrow L_2=6\end{array}$

  $\begin{array}{l}{W}_2=W_1\times k_1\\ \Rightarrow W_2=1\times 3\\ \Rightarrow W_2=3\end{array}$

Therefore,

Dimensions of the iron on at the back of the t-shirt is $6$ inch and $3$ inch.

Now,

The second iron on is enlarged by a scale factor of $2$ for the front of the shirt.

Let $L_3$ inch and $W_3$ inch be the dimensions of the iron on at the front.

  $\begin{array}{l}{L}_3=L_2\times k_2\\ \Rightarrow L_3=6\times 2\\ \Rightarrow L_3=12\end{array}$

  $\begin{array}{l}{W}_3=W_2\times k_2\\ \Rightarrow W_3=3\times 2\\ \Rightarrow W_3=6\end{array}$

Therefore,

Dimensions of the iron on at the front of the t-shirt is $12$ inch and $6$ inch.

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