If a square and a triangle have same perimeter, which has the greater area

Question

Illustrate with examples

Answer 1

The winner of this contest will be the square.

Example: perimeter 4, sides of square all equal 1, area =1.

 

If the same perimeter is assigned to an equilateral triangle, each side will be 4/3 in length, and the triangle's area will be 

(4/9)√3 which is about 0.7698 square units.