Chapter 2.8, Problem 13P

The Finish-Line Company is drawing up plans for a room addition shown below. The addition will include a large bedroom with a bathroom as shown.

a. What are the actual dimensions of the room addition?

b. What are the actual dimensions of the bathroom?

c. What is the actual length of the exterior wall between the end of the room addition and the bathroom wall? This length is represented by $x$.

To determine

To Find: The actual dimensions of the room.

Answer to Problem 13P

The actual dimensions of the room. $\text{=}\left(25\times \text{15}\right){\text{ft}}^2$

Explanation of Solution

Given:

  

Length of the addition room $L=8.33\text{in}$

Breadth of the room $B=5\text{in}$

Scale used, $1\text{in:3}\text{ft}$

Calculation:

Actual length of the room can be given as:

  $\begin{array}{l}\frac{1\text{in}}{\text{3}\text{ft}}=\frac{8.33\text{in}}{X}\\ X=\frac{3\text{ft}}{1\text{in}}\times 8.33\text{in}\\ X=24.99\\ X\approx 25\text{ft}\end{array}$

Actual breadth of the room can be given as:

  $\begin{array}{l}\frac{1\text{in}}{\text{3}\text{ft}}=\frac{5\text{in}}{y}\\ y=\frac{3\text{ft}}{1\text{in}}\times 5\text{in}\\ y=15\text{ft}\end{array}$

Actual dimension of the room addition is

  $\begin{array}{l}=25\text{ft}\times \text{15}\text{ft}\\ \text{=}\left(25\times \text{15}\right){\text{ft}}^2\end{array}$

To determine

To Find: The actual dimensions of the bathroom.

Answer to Problem 13P

The actual dimensions of the bathroom. $\text{=}\left(10\times 8\right){\text{ft}}^2$

Explanation of Solution

Given:

  

Length of the bathroom $L=3.33\text{in}$

Breadth of the bathroom $B=2.67\text{in}$

Scale used, $1\text{in:3}\text{ft}$

Calculation:

Actual length of the bathroom can be given as:

  $\begin{array}{l}\frac{1\text{in}}{\text{3}\text{ft}}=\frac{3.33\text{in}}{x\text{'}}\\ x\text{'}=\frac{3\text{ft}}{1\text{in}}\times 3.33\text{in}\\ x\text{'}=9.99\\ x\text{'}\approx 10\text{ft}\end{array}$

Actual breadth of the bathroom can be given as:

  $\begin{array}{l}\frac{1\text{in}}{\text{3}\text{ft}}=\frac{2.67\text{in}}{y}\\ y=\frac{3\text{ft}}{1\text{in}}\times 2.67\text{in}\\ y=8.01\text{ft}\\ y\approx 8.01\text{ft}\end{array}$

Actual dimension of the room addition is

  $\begin{array}{l}=10\text{ft}\times \text{8}\text{ft}\\ \text{=}\left(10\times 8\right){\text{ft}}^2\end{array}$

To determine

To Find: The actual length of the exterior wall.

Answer to Problem 13P

The actual length of the exterior wall $x=15\text{ft}$

Explanation of Solution

Given:

  

Length of the bathroom $l=3.33\text{in}$

Length of the addition room $L=8.33\text{in}$

Scale used, $1\text{in:3}\text{ft}$

Calculation:

Actual length of the bathroom can be given as:

  $\begin{array}{l}\frac{1\text{in}}{\text{3}\text{ft}}=\frac{3.33\text{in}}{x\text{'}}\\ x\text{'}=\frac{3\text{ft}}{1\text{in}}\times 3.33\text{in}\\ x\text{'}=9.99\\ x\text{'}\approx 10\text{ft}\end{array}$

Actual length of the room can be given as:

  $\begin{array}{l}\frac{1\text{in}}{\text{3}\text{ft}}=\frac{8.33\text{in}}{X}\\ X=\frac{3\text{ft}}{1\text{in}}\times 8.33\text{in}\\ X=24.99\\ X\approx 25\text{ft}\end{array}$

The actual length of the exterior wall can be given as:

  $\begin{array}{l}x=X-x\text{'}\\ x=25\text{ft}-10\text{ft}\\ x=15\text{ft}\end{array}$