if M is the mid point of PQ it means PM + MQ = PQ
7x + 8 + 5x + 20 = PQ
and PM = MQ as the M is the mid point of PQ
7x + 8 = 5x + 20
7x - 5x = 20 - 8
2x = 12
x = 6
it means PQ = 7(6) + 8 + 5(6) + 20
= 42 + 8 + 30 + 20
= 50 + 50 = 100
and PM = MQ = 50