Question

rectangles r and s are similar. if the area of rectangle r is 154, what is the area of rectangle s?
rectangle r
area = 154
22
rectangle s
13.2

Explanation:

Step1: Find the scale factor

The ratio of the corresponding sides (lengths) of similar rectangles is the scale factor. For Rectangle R, length \( l_R = 22 \), for Rectangle S, length \( l_S = 13.2 \). The scale factor \( k=\frac{l_S}{l_R}=\frac{13.2}{22}=0.6 \).

Step2: Relate areas of similar figures

For similar figures, the ratio of their areas is the square of the scale factor. Let \( A_R = 154 \) (area of R) and \( A_S \) (area of S). Then \( \frac{A_S}{A_R}=k^2 \).

Step3: Calculate area of S

Substitute \( A_R = 154 \) and \( k = 0.6 \) into the formula. First, \( k^2=(0.6)^2 = 0.36 \). Then \( A_S=A_R\times k^2=154\times0.36 = 55.44 \).

Answer:

The area of rectangle S is \( 55.44 \).