Question

△dog~△cat
what is the ratio of the area of △dog to the area of △cat?
a $\frac{1}{9}$
b $\frac{2}{5}$
c $\frac{4}{25}$
d $\frac{9}{15}$

Explanation:

Step1: Recall ratio - of - areas formula

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 side lengths of \(\triangle DOG\) to \(\triangle CAT\) be \(k=\frac{6}{15}=\frac{2}{5}\).

Step2: Calculate ratio of 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. \(\frac{4}{25}\)