Question

In the Figure, ∠DFE = 90° , FG ED. If FG = 12, GD = 8, find EG *​

Answer 1

Step-by-step explanation:

We know that ,

In a right angled triangle , the perpendicular segment to the hypotenuse from the opposite vertex, is the geometric mean of the segment into which the hypotenuse is divided .

Here , seg GF⊥segED

∴GF

2

=EG×GD

⇒12

2

=EG×8

⇒144=EG×8

⇒EG=

8

144

⇒EG=18

Hence, EG=18

Now,

According to pythagoras theoram , in △DGF

DG

2

+GF

2

=FD

2

⇒8

2

+12

2

=FD

2

⇒64+144=FD

2

⇒FD

2

=208

⇒FD=4

13

In△EGF

EG

2

+GF

2

=EF

2

⇒18

2

+12

2

=EF

2

⇒324+144=EF

2

⇒EF

2

=468

⇒EF=6

13

Hence, FD=4

13

and EF=6

13

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