Question

1. the area of a carpet in the living room of a house is 72 square feet. if a 1:12 dollhouse has a similar living room with a similar rug, what is the area of the rug in the dollhouse?

Explanation:

Step1: Recall the ratio - area relationship

For similar figures, if the linear - scale factor is \(k\), the ratio of the areas of two similar figures is \(k^{2}\). Here, the linear - scale factor \(k=\frac{1}{12}\) (since it's a 1:12 dollhouse).

Step2: Calculate the area of the rug

Let \(A_1\) be the area of the rug in the dollhouse and \(A_2\) be the area of the carpet in the real - living room. The ratio of the areas of the similar rug (in dollhouse) and carpet (in real living room) is \(k^{2}\), where \(k = \frac{1}{12}\). So \(A_1=A_2\times k^{2}\). Given \(A_2 = 72\) square feet and \(k=\frac{1}{12}\), then \(A_1=72\times(\frac{1}{12})^{2}\).
\[A_1 = 72\times\frac{1}{144}\]
\[A_1 = 0.5\] square feet.

Answer:

0.5 square feet