Answer:
KN = 72
Step-by-step explanation:
ΔKPL and ΔKNM are similar.
∠KLP = ∠KMN (Because PL and NM are parrallel)
∠KPL = ∠KNM (Because PL and NM are parrallel)
∠NKM = ∠PKL (Same angle, Common)
Now, Both the trianlges are similar just there is a size difference.
First we need to find scale factor, therefore:
[tex]\frac{KL}{LM}[/tex] = [tex]\frac{11}{55}[/tex] = [tex]\frac{1}{5}[/tex]
Now we know the scale factor is [tex]\frac{1}{5}[/tex] therefore:
[tex]\frac{KP}{PN}[/tex] = [tex]\frac{PK}{60}[/tex]
To find PK we times 60 by [tex]\frac{1}{5}[/tex] therefore:
Answer is 12
Now KN is PK+ PN threfore:
KN is 72
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