Question

rectangles q and r are similar. if the area of rectangle q is 294, what is the area of rectangle r?

21
rectangle q
area = 294

2.1
rectangle r

Explanation:

Step1: Find the scale factor

The length of Rectangle Q is 21 and the length of Rectangle R is 2.1. The scale factor \( k \) is the ratio of the corresponding sides, so \( k=\frac{2.1}{21} = 0.1\).

Step2: Relate areas of similar figures

For similar figures, the ratio of their areas is the square of the scale factor. Let \( A_Q \) be the area of Rectangle Q and \( A_R \) be the area of Rectangle R. So \( \frac{A_R}{A_Q}=k^2 \).

Step3: Calculate the area of Rectangle R

We know \( A_Q = 294 \) and \( k = 0.1 \), so \( k^2=(0.1)^2 = 0.01 \). Then \( A_R=A_Q\times k^2=294\times0.01 = 2.94 \).

Answer:

The area of rectangle R is \( 2.94 \).