Chapter 11.8, Problem 12IP

To determine

To find: What are the dimensions of the third blanket.

Answer to Problem 12IP

Dimensions of the third blanket is $7.5$ feet by $6$ feet.

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

Explanation of Solution

Given information:

The First measure of blanket is

  $L_1=2.5$ feet.

  $W_1=2$ feet.

First Scale factor $=k_1=2$ to make second Blanket

Second Scale factor $=k_2=1.5$ to make third blanket.

Given

The First measure of blanket is

  $L_1=2.5$ feet.

  $W_1=2$ feet.

Let $L_2$ inch and $W_2$ inch be the dimensions of the Second blanket.

  $\begin{array}{l}{L}_2=L_1\times k_1\\ \Rightarrow L_2=2.5\times 12\\ \Rightarrow L_2=5\end{array}$

  $\begin{array}{l}{W}_2=W_1\times k_1\\ \Rightarrow W_2=2\times 2\\ \Rightarrow W_2=4\end{array}$

Therefore,

Dimensions of the second blanket is $5$ feet by $4$ feet.

Now,

The second blanket is enlarged by a scale factor of $1.5$ to

Let $L_3$ inch and $W_3$ inch be the dimensions of the Third blanket

  $\begin{array}{l}{L}_3=L_2\times k_2\\ \Rightarrow L_3=5\times 1.5\\ \Rightarrow L_3=7.5\end{array}$

  $\begin{array}{l}{W}_3=W_2\times k_2\\ \Rightarrow W_3=4\times 1.5\\ \Rightarrow W_3=6\end{array}$

Therefore,

Dimensions of the third blanket is $7.5$ feet by $6$ feet.

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