Question

If CD is parallel to LA and DE parallel to AC. Find the length of CL if BE=4cm EC= 2cm

Answer 1

a
In ​ΔBCA
ED || CA
BE/BC = BD/BA {Corollary of Basic Proportionality Theorem}
⇒BE /BE+CE = BD/AB
⇒4/(4+2) = BD/AB
⇒4/6 = BD/AB (1)
In ΔBLA
DC || AL
BC/BL = BD/AB {Corollary of Basic Proportionality Theorem}
6/(6 + CE) = BD/AB (2)
Combining Equations (1) and (2)
6/(6 + CE) = 4/6
⇒ 36 = 4(6 + CE)
⇒36 = 24 +4CE
⇒4CE = 36 -24 =12
⇒CE = 12/4
CE = 3 cm

Answer 2

Answer:

Step-by-step explanation:

In ​ΔBCA

ED || CA

BE/BC = BD/BA {Corollary of Basic Proportionality Theorem}

⇒BE /BE+CE = BD/AB

⇒4/(4+2) = BD/AB

⇒4/6 = BD/AB (1)

In ΔBLA

DC || AL

BC/BL = BD/AB {Corollary of Basic Proportionality Theorem}

6/(6 + CE) = BD/AB (2)

Combining Equations (1) and (2)

6/(6 + CE) = 4/6

⇒ 36 = 4(6 + CE)

⇒36 = 24 +4CE

⇒4CE = 36 -24 =12

⇒CE = 12/4

CE = 3 cm