Is the area of a triangle a function of its perimeter?

algebra-precalculus

Solution 1:

A triangle with sides 1,1 and 2 has perimeter 4 and area =0. A triangle with sides all equal to 4/3 has the same perimeter and positive area. Ergo the area is not a function of the perimeter (it is if you restrict to equilateral or other special families)

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