The Solution:
Given:
Required:
To find the perimeter (in inches) of the floor in the scale drawing.
Step 1:
Find the value of x.
By the similarity theorem:
[tex]\frac{14}{x}=\frac{28}{30}[/tex]Cross multiplying, we get:
[tex]\begin{gathered} 28x=14\times30 \\ \\ Dividing\text{ both sides by 28, we get} \\ \\ x=\frac{14\times30}{28}=\frac{30}{2}=15\text{ in.} \end{gathered}[/tex]Step 2:
Find the perimeter, in inches, of the floor in the scale drawing.
By formula, the perimeter is:
[tex]\begin{gathered} P=2(L+W) \\ \text{ Where:} \\ L=14\text{ inches} \\ W=x=15\text{ inches} \\ P=perimeter=? \end{gathered}[/tex]Substituting these values in the formula, we get:
[tex]P=2(14+15)=2\times29=58\text{ inches}[/tex]Therefore, the correct answer is 58 inches.
