Answer:
Step-by-step explanation:
Since, PN ≅ NR
RM ≅ MQ
PL ≅ LQ
QN, LR and PM are the medians and they intersect each other at point K which will be the centroid of ΔPQR.
By the property of centroid,
Point K will divide the medians in the ratio of 2 : 1
By this property,
PK : KM = 2 : 1
4 : KM = 2 : 1
[tex]\frac{4}{KM}=\frac{2}{1}[/tex]
KM = 2
KQ = [tex]\frac{2}{(2+1)}(NQ)[/tex]
= [tex]\frac{2}{3}\times 6[/tex]
KQ = 4
LK : RK = 1 : 2
LK : 3 = 1 : 2
[tex]\frac{LK}{3}=\frac{1}{2}[/tex]
LK = 1.5
LR = LK + RK
= 1.5 + 3
LR = 4.5
NK = [tex]\frac{1}{(2+1)}(QN)[/tex]
= [tex]\frac{1}{3}(6)[/tex]
NK = 6
PM = PK + KM
PM = 4 + 2
PM = 6
