Question

Suppose the length of segment BE is 11 cm. Which is the BEST ESTIMATE for segment GH?

Answer 1

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,

$\dfrac{DB}{DG}=\dfrac{BE}{GH}\\\\\Rightarrow\dfrac{2DG}{DG}=\dfrac{11}{GH}\ \ [{DG=GB,\therefore\ DB=2DG }]$

$\Rightarrow\ \dfrac{2}{1}=\dfrac{11}{GH}\Rightarrow\ GH=\dfrac{11}{2}=5.5\text{ cm}$

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.