## Side of a Square Inscribed in a Diamond

From the diagram the largest square that can be inscribed in a diamond of height
$2h$
and base
$2b$
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
$2(b - \frac{b^2}{h+b}) = \frac{2hb}{h+b}$