To find the lengths of MN and PN, we can first set up a proportion using the ratio given.

Since the ratio of MN to PN is 7:5, we can set up the proportion as follows:

MN/PN = 7/5

Now, we can substitute PN = 12 into the proportion:

MN/12 = 7/5

Cross multiplying, we get:

5MN = 84

Dividing by 5, we get:

MN = 16.8

Now we can calculate PN using the ratio:

PN = 12 - MN
PN = 12 - 16.8
PN = -4.8

Therefore, the lengths of MN and PN are 16.8 and -4.8 respectively.