Question

A triangle EFG has sides 6 cm, 5 cm and 2 cm. The median EX is drawn as shown. Which of the following could be the length of EX? A 6.1 cm B 5.4 cm C 5 cm D 4.8 cm with very good explanation plzz thanks

Answer 1

Given : A triangle EFG has sides 6 cm, 5 cm and 2 cm. The median EX is drawn as shown.

To Find : Which of the following could be the length of EX

Solution:

EX is median

Hence  FX = XG = FG/2 = 2/2 = 1 cm

ΔEFX

EF = 6 cm

FX = 1 cm

EX = ?

Sum of two sides greater than third side

Hence   5  < EX  < 7

ΔEGX

EG = 5 cm

GX = 1 cm

EX = ?

Sum of two sides greater than third side

Hence   4  < EX  < 6

5  < EX  < 7

 4  < EX  < 6

Combining both

5  < EX  < 6

in given options only

5.4 cm lies between 5 & 6 cm

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