To find if the two triangles are similar, we will assume they are similar. If this leads to a contradiction, then the triangles are not similar.
First, if they are similar, the ratios between the corresponding sides of the triangles must be the same:
[tex]\frac{MK}{HM}=\frac{MJ}{GM}=\frac{JK}{GH}[/tex]
From the problem, we identify:
[tex]\begin{gathered} MK=12\text{ cm} \\ HM=8\text{ cm} \\ MJ=16\text{ cm} \\ GM=12\text{ cm} \end{gathered}[/tex]
Then, the ratios are:
[tex]\begin{gathered} \frac{MK}{HM}=\frac{12\text{ cm}}{8\text{ cm}}=\frac{3}{2} \\ \\ \frac{MJ}{GM}=\frac{16\text{ cm}}{12\text{ cm}}=\frac{4}{3} \end{gathered}[/tex]
As we can see, they are not the same, so we conclude that the triangles are not similar.
