A calculus problem by A Former Brilliant Member

Calculus Level 4

The three sides of a triangle are variable in lengths but the perimeter is constant. The maximum possible area of the triangle is 300 square centimeters. What is the perimeter of the triangle in centimeters? Round off your answer to the nearest integer.


The answer is 79.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Marta Reece
Jun 20, 2017

For a given perimeter the triangle with the largest area is equilateral.

300 = 3 4 a 2 300=\dfrac{\sqrt3}4a^2

a = 1200 3 a=\sqrt{\dfrac{1200}{\sqrt3}}

3 a = 3600 ≈ 79 3a=\sqrt{3600}\approx\boxed{79}

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