The small triangle at the bottom right must be right and isosceles, and the angle at the bottom right must be 45°, because the sum of angles is 180°. This means the largest triangle is isosceles, and the bottom length is 4, i.e. the units are \frac{1}{2}.

We begin with z^2 + z^2 = 1 giving z^2 = \frac{1}{2}

The we continue to the left, looking at the small triangle with sides y, c, and 1:

y^2 +  c^2 = 1

y^2 + (5 - c)^2 = 20

b = \frac{2}{ \sqrt{20} }

x^2 + \frac{1}{5} = 1

x^2 = \frac{4}{5}

Similarly we continue for x and w and get

\frac{17}{18}+\frac{5}{4}+\frac{100}{64}+\frac{2}{1} = \frac{47}{8}

1/( (4/5)^2 ) + 1/( (4/3)^2 ) + 1/( (4/2)^2 ) + 1/( (2√2)^2 ) = 5/2