What is the largest square inscribed in an equilateral triangle?

A planar shape or solid that is inscribedin another geometric shape or solid is enclosed and "fitted tightly" within it. Saying "a square is inscribed in a triangle" means exactly the same thing as "a triangle is circumscribed in a square".

The largest square that can be inscribed in an equilateral triangle−

The largest square that can be inscribed in an equilateral triangle−

Let Let’s take an example,

Input: 5
Output: 2.32

explains that one side of the

square is

x.

Now,

AH is perpendicular to DE.

DE is parallel to BC, angle AED = angle ACB = 60

is in triangle

EFC中，

⇒ Sin60 = x/ EC

⇒ √3 / 2 = x/EC

⇒ EC = 2x/√3

at In triangle

AHE,

⇒ Cos 60 = x/2AE

⇒ 1/2 = x/2AE

⇒ AE = x

Sides of a triangle

AC = 2x/√3 x. Now,

a = 2x/√3 x

x = a/(1 2/√3) = 0.464a

Example

Demonstration

#include <stdio.h>
#include <math.h>
int main() {
   float a = 5;
   float area = 0.464 * a;
   printf("The area is : %f",area);
   return 0;
}

Output

The area is : 2.320000

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