Given: klmn is a parallelogram

m∠n=3m∠k,

lf

⊥

kn

,

ld

⊥

nm

kf=2 cm, fn=4 cm

find: lf, ld

how to solve it

The value of LF is 2 cm and LD is 4.24 cm.

Step-by-step explanation:

Given :Parallelogram KLMN

LF  ⊥  KN

LD ⊥  NM

KF = 2 cm, FN = 4 cm

∠N = 3∠K

To find : LF , LD

Solution :

Sum of all angles of parallelogram is 360°.

∠N + ∠K +∠L + ∠M = 360°

∠N + ∠K +∠N + ∠K = 360° (opposites angles are equal in ||gram)

∠3K + ∠K +∠3K + ∠K = 360°

8∠K=360°

∠K = 45°

In triangle KLF

LF = 2 cm

In triangle LMD

LM = KN = 6 cm (Opposites sides are equal in ||gram)

LD = 4.24 cm (approx)

The value of LF is 2 cm and LD is 4.24 cm.