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Find the length of MK if JK=36, JL=48, and JN=60 Answer:

 

 Feb 26, 2021
 #1
avatar+34315 
+1

JM / JK   =JN/JL

JM / 36 = 60/48

JM =   36 * 60 / 48 = 45   units          (obviously not drawn to scale )       MK = JM - 36 = 9

 Feb 26, 2021
edited by ElectricPavlov  Feb 26, 2021
 #2
avatar+32 
+1

We know that $\triangle JKL \sim \triangle JMN$ by $AA$ similarity ($\angle JKL \cong \angle JMN$ and $\angle JLK \cong \angle JNM$ because $KL \parallel MN$). Therefore,

$$\frac{JK}{JM} = \frac{JL}{JN},$$

$$\frac{36}{JM} = \frac{48}{60}, $$

$$JM = 45. $$

Given that $JM=45$, we see that $MK = JM - JK$, and $JK=36$ using the similarity ratio above. Thus, $MK = 45 - 36 = \boxed{9}.$

 Feb 26, 2021

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