Similar triangles.
(h-x)/h=y/a
Y = a (h-x)/h is obtained.
The area of rectangular EFGH is
S=xy=x[a(h-x)]/h=(-a/h)x? +ax,∫-a/h & lt; ∴S has a maximum value.
When x=-a/[2(-a/h)]=h/2,
The maximum area of an inscribed rectangle is S=-a? /[4(-a/h)]=ah/4