Question

in the figure it is given that AB is equal to BC is equal to 5cm if AE is equal to 7cm it is equals to 24 cm the length of DE also show that angle ABE and angle BDCare congruen​

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 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.