in a triangle ABC, D and E are points on the sides AB and AC repectively such that that DE||BC.
If AD=8,AB=12 and AE=12 Find CE
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The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.
It is given that AD=8 cm, AB=12 cm and AE=12 cm.
Using the basic proportionality theorem, we have
AB
AD
=
AC
AE
=
BC
DE
⇒
AB
AD
=
AC
AE
⇒
12
8
=
AC
12
⇒8AC=12×12
⇒8AC=144
⇒AC=
8
144
=18
Now, CE=AC−AE=18−12=6 cm
Hence, CE=6 cm.
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