Answer:
6.6 miles
Step-by-step explanation:
due to the construction with the 3 parallel lines, the two crossing lines create 2 similar triangles (same angles and all side lengths and all other lines are all determined by the same multiplication factor going from one triangle to the other).
so,
LM = KL × f
MP = HK × f
HL = LP × f
KL = LM × f
and so on.
and then, also
JL = LN × f
the other thing we know due to the construction (L will always be connected with the middle of HK and MP) : the triangles are isoceles triangle (2 equal sides). in fact, because HK = HL = 2 miles, and it is an isoceles triangle, we also know that KL = 2 miles too.
so, we have
KL = LM × f
2 = 6 × f
f = 2/6 = 1/3
and therefore
JL = LN × f
2.2 = LN × 1/3
LN = 2.2 / 1/3 = 2.2 × 3/1 = 2.2 × 3 = 6.6
so, LN is 6.6 miles long.
