Question

In the AABC, D and E are points on side AB and AC respectively such that
DE I BC. If AE=2cm, AD=3cm and BD=4.5cm, then find CE.​

Answer 1

Answer:

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.