Steps of construction:
1. Draw a line segment $BC=3.5cm$.
2. With B as a center and radius $5cm$, let’s draw an arc using compass.
3. With C as a center and radius $4cm$, draw another arc using compass, cutting the previous arc at A.
4. So now Join AB and AC.
Then, $\vartriangle ABC$ is the required triangle.
5. With B as center and radius measuring more than half of BC, draw arcs using compass on both sides of BC.
6. With C as center and the same radius as before, draw arcs using compass on both sides of BC, cutting the previous arcs with the help of compass at P and Q, as shown. Now Join PQ.
Then, PQ is the required perpendicular bisector of BC.
Therefore , We get P is the required point which is at equal distance from AB, BC, B and C.
So the Length PB is $2.5cm$.