Since triangle LKJ is similar to triangle LNM,
we know that JK / MN = LK / LN.
JK = 40
MN = 25
LK = LN + KN = LN + 12
LN = ?
Sub these values in and solve for LN...
40 / 25 = (LN + 12) / LN
Simplifying and distributing...
1.6 = 1 + 12 / LN
Subtracting 1 from on both sides...
0.6 = 12 / LN
Multiplying both sides by LN...
0.6 * LN = 12
Dividing both sides by 0.6...
LN = 20
