Answer: C) 5.5 cm.
Step-by-step explanation:
From the given , it can be clearly seen that in triangle DBE , G and H are the midpoints of segment DB and DE respectively.
Also, GH is parallel to BE. [By Converse of Basic proportionality theorem]
Length of BE= 11 cm.
Further more,
[tex]\dfrac{DB}{DG}=\dfrac{BE}{GH}\\\\\Rightarrow\dfrac{2DG}{DG}=\dfrac{11}{GH}\ \ [{DG=GB,\therefore\ DB=2DG }][/tex]
[tex]\Rightarrow\ \dfrac{2}{1}=\dfrac{11}{GH}\Rightarrow\ GH=\dfrac{11}{2}=5.5\text{ cm}[/tex]
Hence, the BEST ESTIMATE for segment GH is 5.5 cm.
Note :
Converse of Basic Proportionality Theorem says that when a line (or a segment) divides any two sides of a triangle in equal proportion then the line ought to be parallel to the remaining third side.
