To solve for the length of arc AB, we need to know the measurement of the central angle that subtends it.
We know the following property:
Solving for x, we get:

So we now know that arc DC meaures 90 degrees.
But arc DC is equal to m∠DYC, and m∠DYC = m∠EYB because they are vertical angles. m∠EYB = arc EB. Therefore arc EB measures 90 degrees.
arc EB = arc EA + arc AB
90 = 50 + arc AB
So arc AB = 90 degrees
We can now use this to solve the length of the arc.

People would have to walk 78.54 units to move from point A to point B along the outside of the garden.