Question

question
rectangles a and b are similar. if the area of rectangle a is 12, what is the area of rectangle b?
rectangle a
area = 12
4
rectangle b
1.6

Explanation:

Step1: Find the scale factor

The corresponding sides of similar rectangles have a ratio. For Rectangle A, the side is 4, and for Rectangle B, it's 1.6. The scale factor \( k \) is \( \frac{1.6}{4}=0.4 \).

Step2: Relate areas of similar figures

For similar figures, the ratio of areas is the square of the scale factor. Let \( A_A = 12 \) (area of A) and \( A_B \) (area of B). The ratio of areas \( \frac{A_B}{A_A}=k^2 \).

Step3: Calculate area of B

First, \( k^2=(0.4)^2 = 0.16 \). Then, \( A_B=A_A\times k^2 = 12\times0.16 = 1.92 \).

Answer:

1.92