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(C) Let the perimeter of the triangle be $P$. According to Heron's formula,the area $A$ of a triangle with sides $a, b, c$ is given by $A = \sqrt{s(s-

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Equilateral triangle

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(C) Let the perimeter of the triangle be $P$. According to Heron's formula,the area $A$ of a triangle with sides $a, b, c$ is given by $A = \sqrt{s(s-a)(s-b)(s-c)}$,where $s = P/2$ is the semi-perimeter.For a fixed $s$,the product $(s-a)(s-b)(s-c)$ is maximized when $s-a = s-b = s-c$,which implies $a = b = c$.Thus,for a given perimeter,the triangle with the maximum area is an equilateral triangle.Alternatively,using the method of Lagrange multipliers or calculus,we find that for a fixed perimeter,the area is maximized when all sides are equal.

For a given perimeter,the triangle having the maximum area is:

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