Answer:
[tex]DM=38\ cm[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
Triangles DEF and OEN are similar by AA Similarity Postulate
Remember that if two triangles are similar, then the ratio of its corresponding sides is proportional
In this problem
[tex]\frac{DE}{OE}=\frac{DF}{ON}[/tex]
substitute the given values
[tex]\frac{44}{22}=\frac{DF}{38}[/tex]
[tex]2=\frac{DF}{38}[/tex]
[tex]DF=2(38)=76\ cm[/tex]
[tex]DF=2DM\\76=2DM\\DM=38\ cm[/tex]
