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Question



In figure,E and F are mid - points of the sides AB and AC respectively of the ΔABC. G and H are mid-points of the sides AE and AF respectively of the ΔAEF. If GH=1.8 cm, find BC.


A

7.2cm

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B

7.6cm

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C

8.2cm

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D

9cm

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Solution

The correct option is D: 7.2 cm

By Midpoint theorem: The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”


E and F are mid-points of sides AB and AC of ΔABC

EFBC, and EF=12BC(i)

G and H are mid-points of sides AB and AC of ΔAEF

GHEF,GH=12EF(ii)

From eq.(ii) and (ii), we have,

GH=12×12BC=14BC

BC=4×GH

=4×1.8 cm=7.2 cm [GH=1.8 cm given]

Hence, BC=7.2 cm


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