Answer:
Step-by-step explanation:
Triangles JKN MLN are similar.
There is a right angle at J and M. <JNK and <MNL are vertically opposite. By AA the triangles are similar.
Find JN
JK = 3
LM = 9
JK/LM = JN/(20 - JN)
3/9 = JN/(20 - JN)
1/3 = JN/(20 - JN)
20 - JN = 3JN
20 = 4JN
JN = 5
NM = 20 - 5
NM = 15
Find KN
KN^2 = JN^2 + JK^2
JK = 3
JN = 5
KN = ?
KN^2 = JK^2 + JN^2
KN^2 = 3^2 + 5^2
KN^2 = 34
KN = sqrt(34)
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Find LN
LN = ?
MN = 15
LM = 9
LN = sqrt(15^2 + 9^2)
LN = sqrt(306)
LN = 3*sqrt(34)
Find LK
LK = sqrt(34) + 3sqrt(34)
LK = 4 sqrt(34)
