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# help similar triangles

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

Feb 26, 2021

#1
+30571
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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
+32
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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