Mathematics

Problem

For a triangle with fixed perimeter

P

, the quantity

s(s-a)(s-b)(s-c)

in Heron’s formula attains its maximum value when which of the following conditions is satisfied? a) Exactly two sides are equal b)

a=b=c

a^{2}+b^{2}=c^{2}

d) One side equals

\dfrac{P}{2}