MathDB

square has maximum area... isi 2012 #6

Source:

May 13, 2012

geometryperimetercalculusconicsellipseinequalitiesperpendicular bisector

Problem Statement

i) Let

0<a<b

.Prove that amongst all triangles having base

a

and perimeter

a+b

the triangle having two sides(other than the base) equal to

\frac {b}{2}

has the maximum area.
ii)Using

i)

or otherwise, prove that amongst all quadrilateral having give perimeter the square has the maximum area.