Chapter 11, Problem 34CR

To determine

To find: What are the dimensions of the largest print.

Answer to Problem 34CR

Dimensions of the largest print is $36$ inch by $45$ inch.

Explanation of Solution

Given information:

The Original dimensions of the print is

  $L_1=8$ inch.

  $W_1=10$ inch.

First Scale factor for enlarging original print $=k_1=1.5$

Second Scale factor $=k_2=3$

Given

The Original dimensions of the print is

  $L_1=8$ inch.

  $W_1=10$ inch.

Let $L_2$ inch and $W_2$ inch be the dimensions of the photo print.

  $\begin{array}{l}{L}_2=L_1\times k_1\\ \Rightarrow L_2=8\times 1.5\\ \Rightarrow L_2=12\end{array}$

  $\begin{array}{l}{W}_2=W_1\times k_1\\ \Rightarrow W_2=10\times 1.5\\ \Rightarrow W_2=15\end{array}$

Therefore,

Dimensions of the second image photo print is $12$ inch and $15$ inch.

Now,

The second image is enlarged by a scale factor of $3$ .

Let $L_3$ inch and $W_3$ inch be the dimensions of the largest print.

  $\begin{array}{l}{L}_3=L_2\times k_2\\ \Rightarrow L_3=12\times 3\\ \Rightarrow L_3=36\end{array}$

  $\begin{array}{l}{W}_3=W_2\times k_2\\ \Rightarrow W_3=15\times 3\\ \Rightarrow W_3=45\end{array}$

Therefore,

Dimensions of the largest print is $36$ inch by $45$ inch.