Side of a Square Inscribed in a Diamond

From the diagram the largest square that can be inscribed in a diamond of height  
  and base  
  with vertex at the origin as shown will be foumd from the intersection of the lines  
\[y= \frac{h}{b} x, \: y= -x+b\]

\[\frac{h}{b} x=-x+b \rightarrow x( \frac{h}{b} + 1) = b \rightarrow x=\frac{b^2}{h+b} \]

The square will be of side  
\[2(b - \frac{b^2}{h+b}) = \frac{2hb}{h+b}\]