Question

ac is parallel to bd and ce parallel to df ,if oa=12cm, ab=9cm,oc=8cm and ef=4.5cm find oe
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Answer 1

Step-by-step explanation:

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.

In △OBD, AC∣∣BD, OA=12 cm, AB=9 cm and OC=8 cm.

Using the basic proportionality theorem, we have

BA

OA

=

DC

OC

⇒

9

12

=

DC

8

⇒12DC=8×9

⇒12DC=72

⇒DC=

12

72

=6

Now, in △ODF, CE∣∣DF, EF=4.5 cm, DC=6 cm and OC=8 cm.

Using the basic proportionality theorem, we have

DC

OC

=

EF

OE

⇒

6

8

=

4.5

OE

⇒6OE=8×4.5

⇒6OE=36

⇒OE=

6

36

=6

Hence, OE=6 cm.