Question

In the given figure,DE//AB AD=7CM,CD= 5CM,BC=18CM.FIND BD ??

Answer 1

Thus BE = 10.5 cm and CE = 7.5 cm

Step-by-step explanation:

The correct question is :

In the adjoining figure, DE || AB, AD = 7 cm, CD = 5 cm and BC = 18 cm. Find BE and CE.

Given :

DE ║ AB, AD = 7 cm, CD = 5 cm, BC = 18 cm,

To Find : BD

Applying basic proportionality theorem we get,

$\frac{\text{CD}}{\text{CA}} = \frac{\text{DE}}{\text{AB}} =\frac{\text{CE}}{\text{CB}}$

⇒ $\frac{\text{CD}}{\text{CA}} = \frac{\text{CE}}{\text{CB}}$

⇒ $\frac{5}{12}= \frac{\text{CE}}{18}$

⇒ 18 x 5 = 12CE

CE = $\frac{90}{12} = 7.5 \text{cm}$

As CE = 7.5 cm

CB = CE + EB

18 = 7.5 + EB

EB = 18 - 7.5 = 10.5

Hence, BE = 10.5 cm and CE = 7.5 cm

To Learn More....

1. A quadrilateral abcd circumscribes a circle and ab=6cm, cd=5cm and ad=7cm. the length of side bc is

https://brainly.in/question/4103481

2. In Figure, a circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

https://brainly.in/question/1914235

Answer 2

Given :

DE is parallel to AB

AD = 7 cm

CD = 5 cm

BC = 18 cm

To find :

The value of the side BE

Solution :

Basic proportionality theorem :

A line passing through two sides  of a triangle and parallel to the third side then it divides the two sides into two equal ratios.

AC = CD + AD

      = 5 + 7

      = 12 cm

AC = 12 cm

By using basic proportionality theorem we get :

$\frac{CD}{AD} = \frac{CE}{BE}$

By adding 1 on both the sides we get :

$\frac{CD}{AD} + 1 = \frac{CE}{BE} + 1$

$\frac{CD + AD}{AD} = \frac{CE + BE}{BE}$--------(1)

CD + AD = AC-------(2)

CE + BE = BC ---------(3)

Substitute the values of (2) and (3) in (1)

$\frac{AC}{AD} = \frac{BC}{BE}$

From given values

AC = 12 cm

AD = 7 cm

CD = 5 cm

BC = 18 cm

Now substitute the above values

$\frac{AC}{AD} = \frac{BC}{BE}$

$\frac{12}{7} = \frac{18}{BE}$

$BE = \frac{(18)(7)}{12}$

      = $\frac{21}{2}$

      = 10.5 cm

BE = 10.5 cm

Hence, the value of BE is 10.5 cm.