Question

the figures below are similar. the labeled sides are corresponding.

image of two rectangles, one green (larger) labeled 6 mm on the base, one purple (smaller) labeled 4 mm on the base

what is the ratio of the area of the larger rectangle to the area of the smaller rectangle?
write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Find the ratio of the corresponding sides

The ratio of the corresponding sides of the larger rectangle to the smaller rectangle is \(8:4 = 2:1\).

Step2: Use the property of the ratio of areas of similar figures

For similar figures, if the ratio of corresponding side lengths is \(a:b\), the ratio of their areas is \(a^{2}:b^{2}\). Here \(a = 2\) and \(b = 1\), so the ratio of the areas is \(2^{2}:1^{2}\).

$$2^{2}:1^{2}=4:1$$

Answer:

\(4:1\)