Given that AD=AB and AP = BD x 2, we know that AD = AB = x and BD = y.

Since AD = AB, we can say that x = x + y (since AP = BD x 2)
=> 2y = x

Given that P = 85 cm, we can say that P = 2x + 2y
=> 85 = 2x + 2y
=> 85 = 2(x + y)
=> 85 = 2(x) [since x = 2y]
=> x = 85/2
=> x = 42.5 cm

Now, we can find the value of y:
y = x/2
=> y = 42.5/2
=> y = 21.25 cm

Therefore, AD = AB = x = 42.5 cm
and BD = y = 21.25 cm

So, the measurements are:
AD = AB = 42.5 cm
BD = 21.25 cm