Question

the figures below are similar. the labeled sides are corresponding.
what is the ratio of the area of the larger triangle to the area of the smaller triangle?
write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Find the ratio of corresponding sides

The ratio of the corresponding sides of the larger triangle to the smaller triangle is \(\frac{8}{4}=2\).

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

For similar figures, if the ratio of corresponding side lengths is \(k\), the ratio of their areas is \(k^{2}\). Here \(k = 2\), so the ratio of the areas is \(2^{2}=\frac{4}{1}\).

Answer:

\(4:1\)