Question

write five ratios of the short side to the long side. 4

Explanation:

Step1: Identify short and long sides of first triangle

In $\triangle ABC$, short side is 6, long - side is 9. Ratio is $\frac{6}{9}=\frac{2}{3}$.

Step2: Identify short and long sides of second triangle

In $\triangle DEF$, short side is 12, long - side is 16. Ratio is $\frac{12}{16}=\frac{3}{4}$.

Step3: Find other possible ratios

We can also consider the reciprocals. For $\triangle ABC$, ratio of long - side to short - side is $\frac{9}{6}=\frac{3}{2}$. For $\triangle DEF$, ratio of long - side to short - side is $\frac{16}{12}=\frac{4}{3}$. Another ratio could be comparing the short - side of $\triangle ABC$ to the long - side of $\triangle DEF$, which is $\frac{6}{16}=\frac{3}{8}$, and comparing the long - side of $\triangle ABC$ to the short - side of $\triangle DEF$, which is $\frac{9}{12}=\frac{3}{4}$.

Answer:

$\frac{2}{3},\frac{3}{4},\frac{3}{2},\frac{4}{3},\frac{3}{8}$