Answer:
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
[tex]\tan 45^o=\frac{LF}{KF}[/tex]
[tex]1=\frac{LF}{2 cm}[/tex]
LF = 2 cm
In triangle LMD
LM = KN = 6 cm (Opposites sides are equal in ||gram)
[tex]\Sin 45^o=\frac{LD}{LM}[/tex]
[tex]0.7071 =\frac{LD}{6 cm}[/tex]
LD = 4.24 cm (approx)
The value of LF is 2 cm and LD is 4.24 cm.
