Chapter 7.7, Problem 3CYP

To determine

To find an appropriate scale for the drawing and determine the dimensions of the drawing.

Answer to Problem 3CYP

  $8\times 9.3\text{ in}$

Explanation of Solution

Given:

The scale drawing of her room on an $8.5$ -by- $11$ -inch sheet of paper. If her room is $14$ feet by $12$ feet

Calculation:

Finding the scale of the model as follows-

Now let us apply the proportion rule-

  $\begin{array}{l}\frac{14\text{ ft}}{11\text{ in}}\text{ =1}\text{.27 ft/inch}\\ \frac{12\text{ ft}}{\text{8}\text{.5 in}}\text{ =1}\text{.41 ft/inch}\\ \Rightarrow \text{scale}\approx \text{1}\text{.5ft/inch}\end{array}$

Now actual $=$ scale $\times$ model

  $\begin{array}{l}\frac{14}{1.5}\text{ =}\frac{1.5m}{1.5}\\ m=\mathrm{9.33.}\\ \frac{12}{1.5}\text{ =}\frac{1.5m}{1.5}\\ m=8\end{array}$

Therefore, the dimensions of the model $=8\times 9.3$