Maximum Size of Square Inscribed in Right Angled Triabgle of Given Base and Height
The diagram shows a square inscribed inside a right angled triangle.
The equation of the line from O to C is
\[y=x\]
anf the equation of the line BH is
\[y= - \frac{h}{b} x + h\]
. From these we can write
\[c=- \frac{h}{b}c + h\]
,br> Hence
\[c(1+ \frac{h}{b})=h \rightarrow c= \frac{hb}{h+b}\]
.
The square has side
\[ \frac{hb}{h+b}\]
.
