Heron's formula for the area A of a triangle with sides of length a, b, c > 0 is A = √√s(s − a)(s – b)(s - c), where s = - - Use the method of Lagrange multipliers a+b+c 2 Show that for a given fixed perimeter P = 2s of the triangle, the area is maximised when the triangle is equilateral.

Heron's formula for the area A of a triangle with sides of length a, b, c > 0 is A = √√s(s − a)(s – b)(s - c), where s = - - Use the method of Lagrange multipliers a+b+c 2 Show that for a given fixed perimeter P = 2s of the triangle, the area is maximised when the triangle is equilateral.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.2: The Law Of Cosines

Problem 47E

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Question

Heron's formula for the area A of a triangle with sides of length a, b, c > 0 is
A = √√s(s − a)(s – b)(s - c), where s =
-
-
Use the method of Lagrange multipliers
a+b+c
2
Show that for a given fixed perimeter P = 2s of the triangle, the area is
maximised when the triangle is equilateral.

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