In the pulley system shown in this figure, mq = 30 mm, np = 10 mm, and qp = 21 mm. find mn.

The picture in the attached figure

step 1
Draw a line PT parallel to MN such that T lies on MQ
see the attached figure N 2
Then
TQ = MQ - NP = 30-10 = 20 mm
TP=MN

step 2
in the right triangle PTQ
TQ=20 mm
QP=21 mm
TP=?

applying the Pythagoras Theorem
TP²=TQ²+QP²-----> 20²+21²-----> 841
TP=√841------> TP=29 mm
MN=TP----------> MN=29 mm

the answer is
MN=29 mm

Ithink the answer is: it is likely.