The apothem must satisfy x/y = z/y so:
30/y = y/40
cross multiply
y^2 = 1200
y = 1200^.5
x^2 = 1200 + 900
x^2 = 2100
x = 2100^.5
z^2 = 1600 + 1200
z^2 = 2400
z = 2400^.5
x = 2100^.5, y = 1200^.5, z = 2400^.5
