MathDB

Maximizing Triangle Area

Source:

August 8, 2024

algebrageometryoptimization2022

Problem Statement

For positive real numbers

a

and

b,

let

f(a,b)

denote the real number

x

such that area of the (non-degenerate) triangle with side lengths

a,b,

and

x

is maximized. Find

\sum_{n=2}^{100}f\left(\sqrt{\tbinom{n}{2}},\sqrt{\tbinom{n+1}{2}}\right).