In the pulley system shown in this figure, mq = 12 cm, np = 3 cm, and qp = 40 cm. find mn? -38 cm -41 cm -35 cm -39 cm

Short Answer B

Comment
The trick is to draw a line through N that is parallel to QP That line will be 40 cm long. Call it NQ'.

Step One
Find QQ'
After you have drawn the line parallel to QP that is 40 cm long, label the intersect point of Q'P as Q'. Now you job is to figure out the length of Q'Q. It the lines are parallel, then Q'Q is 3cm -- the same length as NP. 

Step Two
Find the length of MQ'
MQ' = MQ - QQ'
MQ' = 12 - 3
MQ' = 9

Step 3
Find the Length of NQ'
By construction NQ' = 40 cm.

Step Four
Find the length of MN
Use the Pythagorean Theorem. 
MN^2 = Q'M^2 + Q'N^2
Q'M = 9
Q'N = 40
MN^2 = 9^2 + 40^2
MN^2 = 81 + 1600
MN^2 = 1681
MN = sqrt(1581)
MN = 41 <<< answer.