Question

In the figure if AD=7, BD=5, AC=18 find AE AND EC​

Answer 1

Answer:

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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.

It is given that DE∣∣AB,AD=7 cm, CD=5 cm and BC=18 cm.

Using the basic proportionality theorem, we have

CA

CD

=

AB

DE

=

CB

CE

⇒

CA

CD

=

CB

CE

⇒

12

5

=

18

CE

⇒18×5=12CE

⇒12CE=90

⇒CE=

12

90

=7.5

Since CE=7.5 cm, therefore,

CB=CE+EB

⇒18=7.5+EB

⇒EB=18−7.5=10.5

Hence, BE=10.5 cm and CE=7.5 cm