Solution:-
From the given figure, CD || LA and DE || AC,
Consider the ∆BCA,
BE/BC = BD/BA
By using the corollary of basic proportionality theorem,
BE/(BE + EC) = BD/AB
4/(4 + 2) = BD/AB … [equation (i)]
Then, consider the ∆BLA
BC/BL = BD/AB
By using the corollary of basic proportionality theorem,
6/(6 + CL) = BD/AB … [equation (ii)]
Now, combining the equation (i) and equation (ii), we get
6/(6 + CL) = 4/6
By cross multiplication we get,
6 x 6 = 4 x (6 + CL)
24 + 4CL = 36
4CL = 36 – 24
CL = 12/4
CL = 3 cm
Therefore, the length of CL is 3 cm.