Question

How do I solve this problem?

Answer 1

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:

$\frac{KL}{LM}$ = $\frac{11}{55}$ = $\frac{1}{5}$

Now we know the scale factor is  $\frac{1}{5}$ therefore:

$\frac{KP}{PN}$ = $\frac{PK}{60}$

To find PK we times 60 by $\frac{1}{5}$ therefore:

Answer is 12

Now KN is PK+ PN threfore:

KN is 72

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