Points O and N are midpoints of the sides of triangle DEF. Triangle D E F is cut by line segment O N. Point O is the midpoint of side E D and point N is the midpoint of side E F. The lengths of E O and O D are 22 centimeters. The lengths of E N and N F are 30 centimeters. The length of O N is 38 centimeters. Line segments D M and M F are congruent.

What is DM?

22 cm
30 cm
38 cm
76 cm

DM=38\ cmDM=38 cm

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

\frac{DE}{OE}=\frac{DF}{ON}

OE

DE

=

ON

DF

substitute the given values

\frac{44}{22}=\frac{DF}{38}

22

44

=

38

DF

2=\frac{DF}{38}2=

38

DF

DF=2(38)=76\ cmDF=2(38)=76 cm

\begin{gathered}DF=2DM\\76=2DM\\DM=38\ cm\end{gathered}

DF=2DM

76=2DM

DM=38 cm

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C

Step-by-step explanation: