The Mathematics Education Department
EMT 725, Lisa F. Garey

Maximum area -- Triangle

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Here is a common calculus problem solved using a novel approach -- the A.M.-G.M. inequality.

Heron's formula for the area of a triangle is sqrt (s(s-a)(s-b)(s-c)) where s= half perimeter and a,b,c are the 3 sides of the triangle.

We have

By the A.M.-G.M. inequality,

with equality iff a=b=c. Thus, max. area of triangle=

Hence, the area of the triangle is maximized when the sides are all congruent or when it is equilateral.

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