Chapter 5.8, Problem 7IP

(a)

To determine

To find: The actual dimension of the living room from the given floor plan if the scale is $1\text{inch}=24\text{feet}$ .

Answer to Problem 7IP

The actual dimension of the living room is $15\text{feet}$ by $18\text{feet}$ .

Explanation of Solution

Given information:

The scale is $1\text{inch}=24\text{feet}$ . The model width of the living room $\frac{5}{8}\text{inches}$ and the model length is $\frac{3}{4}\text{inches}$ .

Calculation:

Let the width of the living roombe $x$ .Solve the proportion of actual width and the model width.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{24\text{feet}}=\frac{\frac{5}{8}\text{in}\text{.}}{x\text{feet}}\\ x=\frac{5}{8}\times 24\\ =15\end{array}$

Hence, the actual width of the living room is $15\text{feet}$ .

Let the length of the living room be $x$ .Solve the proportion of actual length and the model length.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{24\text{feet}}=\frac{\frac{3}{4}\text{in}\text{.}}{x\text{feet}}\\ x=\frac{3}{4}\times 24\\ =18\end{array}$

Therefore, the actual dimension of the living room is $15\text{feet}$ by $18\text{feet}$ .

(b)

To determine

To find: The actual dimension of the deck from the given floor plan if the scale is

  $1\text{inch}=24\text{feet}$ .

Answer to Problem 7IP

The actual dimension of the deck is $30\text{feet}$ by $9\text{feet}$ .

Explanation of Solution

Given information:

The scale is $1\text{inch}=24\text{feet}$ . The model length of the deck is $1\frac{1}{4}\text{inches}$ and the model width is $\frac{3}{8}\text{inches}$ .

Calculation:

Let the length of the deck be $x$ .Solve the proportion of actual length and the model length.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{24\text{feet}}=\frac{1\frac{1}{4}\text{in}\text{.}}{x\text{feet}}\\ x=\frac{5}{4}\times 24\\ =30\end{array}$

Hence, the actual length of the deck is $30\text{feet}$ .

Let the width of the deckbe $x$ .Solve the proportion of actual width and the model width.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{24\text{feet}}=\frac{\frac{3}{8}\text{in}\text{.}}{x\text{feet}}\\ x=\frac{3}{8}\times 24\\ =9\end{array}$

Therefore, the actual dimension of the deck is $30\text{feet}$ by $9\text{feet}$ .

(c)

To determine

To find: The actual dimension of the kitchen from the given floor plan if the scale is $1\text{inch}=24\text{feet}$ .

Answer to Problem 7IP

The actual dimension of the kitchen is $9\text{feet}$ by $18\text{feet}$ .

Explanation of Solution

Given information:The scale is $1\text{inch}=24\text{feet}$ . The model width of the kitchen $\frac{3}{8}\text{inch}$ .

Calculation:

The model length of the kitchen can be calculated from the dimension,

  $1\frac{1}{4}-\frac{1}{2}=\frac{3}{4}\text{inch}$

Let the actual width of the kitchen be $x$ .Solve the proportion of actual width and the model width.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{24\text{feet}}=\frac{\frac{3}{8}\text{in}\text{.}}{x\text{feet}}\\ x=\frac{3}{8}\times 24\\ =9\end{array}$

Hence, the actual width of the kitchen is $9\text{feet}$ .

Let the actual length of the kitchen be $x$ .Solve the proportion of actual length and the model length.

  $\begin{array}{c}\frac{1\text{in}\text{.}}{24\text{feet}}=\frac{\frac{3}{4}\text{in}\text{.}}{x\text{feet}}\\ x=\frac{3}{4}\times 24\\ =18\end{array}$

Therefore, the actual dimension of the kitchen is $9\text{feet}$ by $18\text{feet}$ .