Herons Formula states that the area of a triangle with sides of lengths and is given by

Chapter 13, Problem 1

(choose chapter or problem)

Herons Formula states that the area of a triangle with sides of lengths and is given by where as shown in the figure. (a) Use Herons Formula to find the area of the triangle with vertices and (b) Show that among all triangles having a fixed perimeter, the triangle with the largest area is an equilateral triangle. (c) Show that among all triangles having a fixed area, the triangle with the smallest perimeter is an equilateral triangle.

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