Question

i) In ∆ ABC, D and E are points on the sides
AB and AC respectively such that DE II BC.
If AB=6.75 cm, AC=8.50 cm and EC=6.8 cm,
then find BD​

Answer 1

Answer:

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=6 cm, DB=9 cm and AE=8 cm.

Using the basic proportionality theorem, we have

AB

AD

=

AC

AE

=

BC

DE

⇒

AB

AD

=

AC

AE

⇒

15

6

=

AC

8

⇒6AC=15×8

⇒6AC=120

⇒AC=

6

120

=20

Hence, AC=20 cm.