what triangular region with p=100 has the most area? find all five triangular regions with p=100 having integer side and integer area . such as 29,29,42
The question is much too vague.
I assume that p is the perimeter (p is not defined)
Are the sides to be integer value?
Are the triangles scalene ? , isosceles ?
The largest triangle of course would be an equilateral triangle with sides 100/3 each and an area of
(1/2)(100/3)^2 sin60°
= (10000/18)(√3/2)
= (2500√3)/9