Dec 4, 2013 · Using Lagrange multipliers, it can be shown that a triangle with given perimeter has the maximum possible area, if it is equilateral. Is there a simple geometric proof of that fact ?

Nov 24, 2019 · The square of maximum area occurs when upper corners of square touches the sides of the equilateral triangle and the bottom side of the square is on one side of the triangle. …

Aug 5, 2025 · The equilateral triangle $ABC$ is subdivided into five smaller triangles as shown in the figure. The areas of three of these triangles are indicated inside them: $ EBF=18 cm^2$, $ …

Mar 11, 2016 · Yes. If you're familiar with construction using compass and straight edge, one of the easiest ways to construct an equilateral triangle is to draw two circles where each circle's …

Aug 13, 2019 · We have an equilateral triangle and want to inscribe a square, in such way that maximizes the area of the square. I sketched two possible ways, not to scale and not perfect. …

Dec 8, 2019 · An equilateral triangle has three sides of equal length and three internal angles which are each $60^\circ$. Imagine cutting the equilateral triangle in half by an altitude.

Feb 18, 2016 · Hint: draw radii that are perpendicular to each side. That will cut up the triangle into 3 smaller triangles whose areas are relatively easy to deduce.

Aug 25, 2011 · How can I find the maximum area possible of equilateral triangle that inside a square whose sides have length a. And how does that triangle look like? Can we construct it …

How do you prove that How do you prove that for any equilateral triangle with side length s, area is $\\frac{s^2 √3}{4}$ ? I tried using an equilateral triangle in a square, but I keep coming up wit...

Jun 8, 2013 · See also Maximal area of a triangle and Proving the regular n-gon maximizes area for fixed perimeter.