Let T be a triangle with side lengths a, b, and c. Thesemiperimeter of T is defined to be s = 1/2(a + b + c).Heron’s formula for the area A of a triangle isA = √s(s − a)(s − b)(s − c).Use Heron’s formula and the method of Lagrange multipliers to prove that, for a triangle with perimeter P, the equilateral triangle maximizes the area.

Let T be a triangle with side lengths a, b, and c. Thesemiperimeter of T is defined to be s = 1/2(a + b + c).Heron’s formula for the area A of a triangle isA = √s(s − a)(s − b)(s − c).Use Heron’s formula and the method of Lagrange multipliers to prove that, for a triangle with perimeter P, the equilateral triangle maximizes the area.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter81: Introduction To Computer Numerical Control (cnc)

Section: Chapter Questions

Problem 4A: A rectangular solid has length L=12.6 mm, width W=23.8 mm, and height H=32.5 mm. Find the length of...

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Question

Let T be a triangle with side lengths a, b, and c. The
semiperimeter of T is defined to be s = 1/2(a + b + c).
Heron’s formula for the area A of a triangle is
A = √s(s − a)(s − b)(s − c).
Use Heron’s formula and the method of Lagrange multipliers to prove that, for a triangle with perimeter P, the equilateral triangle maximizes the area.

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