Question

in the adjoining figure if DE||AB AD = 7 cm CD = 5 cm BC = 18 cm. BE is equal to​

Answer 1

$\red{A}\pink{N}\orange{S}\green{W}\blue{E}\gray{R}$

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

CD/CA=DE/AB=CE/CB

⇒CD/CA=CE/CB

⇒5/12=CE/18

⇒18×5=12CE

⇒12CE=90

⇒CE= 90/12 =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.

Answer 2

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

CD/CA=DE/AB=CE/CB

⇒CD/CA=CE/CB

⇒5/12=CE/18

⇒18×5=12CE

⇒12CE=90

⇒CE= 90/12 =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.