△PBQ perimeter =PB+BQ+PQ. No matter where the point P is, the value of BQ is constant and fixed.

Then, find the minimum value of PB+PQ.

The minimum value of PB+PQ is to turn the problem into the same straight line, turn two line segments into one line segment, and get the result with the shortest line segment between two points.

Solution: the intersection of DQ and AC is p followed by PB.

Then Pb = PD (△ CPB △ CPD)

∴PB+PQ=PD+PQ=DQ

∫ square ABCD, point q is the midpoint of BC side.

∴DQ？ =QC？ +CD？ = 1? +2?

DQ=√5

△PBQ perimeter =PB+BQ+PQ=√5+BQ=√5+ 1