Question

In a figure AC||BD And CE||DF. if OA= 12cm,AB = 9cm, OC = 8cm and EF = 4.5cm, then find FO ?

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Answer 1

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

$\frac{oa}{ba} = \frac{oc}{dc}$

$\frac{12}{9} = \frac{8}{dc}$

$12dc = 8 \times 9 \\ \\ 12dc = 72 \\ dc = \frac{12}{72} = 6$

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

Using the basic proportionality theorem, we have

$\frac{oc}{dc} = \frac{oe}{ef} \\ \\ \frac{8}{6} = \frac{oe}{4.5} \\ \\ ⇒6oe=8×4.5 \\ ⇒6oe=36 \\ \\ \\ oe = \frac{6}{36} \\answer = 6$