Question

△dog∼△cat
what is the ratio of the area of △dog to the area of △cat?
a. $\frac{1}{9}$
b. $\frac{2}{3}$
c. $\frac{4}{25}$
d. $\frac{9}{16}$

Explanation:

Step1: Recall the ratio - of - areas formula for similar triangles

For two similar triangles, if the ratio of their corresponding side lengths is \(k\), the ratio of their areas is \(k^{2}\). Let the ratio of the corresponding side lengths of \(\triangle DOG\) and \(\triangle CAT\) be \(k=\frac{DO}{CA}\). Given \(DO = 6\) and \(CA=15\), then \(k=\frac{6}{15}=\frac{2}{5}\).

Step2: Calculate the ratio of the areas

The ratio of the area of \(\triangle DOG\) to the area of \(\triangle CAT\) is \(k^{2}\). Substitute \(k = \frac{2}{5}\) into \(k^{2}\), we get \(k^{2}=(\frac{2}{5})^{2}=\frac{4}{25}\).

Answer:

C. \(\frac{4}{25}\)