Question

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

A) 4 cm
B) 4.5 cm
C) 5.5 cm
D) 6.5 cm
E) 7 cm

Answer 1

Answer: C) 5.5 cm.

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,

`(DB)/(DG)=(BE)/(GH)\\\\\Rightarrow(2DG)/(DG)=(11)/(GH)\ \ [{DG=GB,\therefore\ DB=2DG }]`

`\Rightarrow\ (2)/(1)=(11)/(GH)\Rightarrow\ GH=(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.