To answer this question, we can proceed as follows:
As we can see from the above figure, the triangles PQR and MQN are similar triangles. If they are similar, then their corresponding sides are in proportion. Then, we have:
[tex]\frac{PR}{MN}=\frac{RQ}{NQ}\Rightarrow\frac{15}{MN}=\frac{10}{2}[/tex]
Then, we need to solve the equation for MN, then we have:
[tex]\frac{15}{MN}=5\Rightarrow\frac{MN}{15}=\frac{1}{5}\Rightarrow MN=\frac{15}{5}\Rightarrow MN=3\operatorname{cm}[/tex]
Therefore, the value for the side MN is 3 cm (option b).
