Question

In the figure given in the attachment, CD || LA and DE || AC. Find the length of CL if BE = 4 cm and EC = 2 cm.​

Answer 1

Answer:

• CL = 3 cm

Explanation:

In this question, we will use the concept of basic proportionality theorem which in short also written as BPT in books.

According to this theorem, if in a triangle, a line which is parallel to one side of a triangle and joins two different sides, then that line divides those sides in proportion.

The theorem would be more clear to you by its application!

We are given that ED || AC

By applying BPT, we get :

⇒ BE / EC = BD / AD

by substituting the given values we get :

⇒ 4 cm / 2 cm = BD / AD

⇒ 2 cm = BD / AD ______ ( Equation 1 )

_________________

Also, we are given that CD || AL

By applying BPT, we get :

⇒ BC / CL = BD / AD

By substituting the given values, we get :

⇒ (BE + CE)/CL = BD / AD

⇒ ( 4cm + 2cm)/ CL = BD / AD

⇒ 6cm / Cl = BD / AD

Now using (equation 1)

⇒ 6cm / CL = 2cm

By rearranging, we get :

⇒ 6 cm / 2 cm = CL

⇒ 3 cm = CL

Hence the required value of CL is 3 cm.

Hope it helps :)

Answer 2

DE || AC

By BPT

BE/EC = BD/AD

2 = BD / AD

CD || LA

BC/CL = BD/AD

6/CL = 2

CL = 6/2

CL = 3

Therefore CL = 3.