We find the length of PQ as 20.
We are given that the points P, Q, and R are collinear.
Also,
Q is in between the points P and R
PQ = 3 a + 11
PR = 18 a - 16
QR = 5 a + 3
We have to find PQ.
Now we know that:
PQ + QR = PR
3 a + 11 + 5 a + 3 = 18 a - 16
8 a + 14 = 18 a - 16
18 a - 8 a = 16 + 14
10 a = 30
a = 3
Putting it in PQ to find its value:
PQ = 3 a + 11
PQ = 3 (3) + 11
PQ = 9 + 11
PQ = 20.
Therefore, we find the length of PQ as 20.
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