Question

a floor plan for a new home shows a rectangular living room with a width of 2 inches and a length of 3.2 inches. the homeowners measured the actual width as 15 feet and the actual length as 28 feet. part a: set up a proportion that could be used to determine similarity. (2 points) part b: using your proportion from part a, determine if the actual living room is similar to the floor plan. show all necessary steps. (2 points)

Explanation:

Step1: Set up the proportion

For similar rectangles, the ratios of corresponding sides are equal. Let the width of the floor - plan be $w_1 = 2$ inches, length of the floor - plan be $l_1=3.2$ inches, actual width be $w_2 = 15$ feet, and actual length be $l_2 = 28$ feet. The proportion is $\frac{w_1}{w_2}=\frac{l_1}{l_2}$, or $\frac{2}{15}=\frac{3.2}{28}$.

Step2: Cross - multiply the proportion

Cross - multiplying the proportion $\frac{2}{15}=\frac{3.2}{28}$ gives $2\times28=15\times3.2$.
Calculate the left - hand side: $2\times28 = 56$.
Calculate the right - hand side: $15\times3.2=48$.
Since $56
eq48$, the actual living room is not similar to the floor plan.

Answer:

Part A: $\frac{2}{15}=\frac{3.2}{28}$
Part B: The actual living room is not similar to the floor plan.