等边三角形内可内接的最大正方形

原文:https://www . geesforgeks . org/等边三角形内可内接的最大正方形/

这里给出的是边长为 a 的等边三角形。任务是找到最大的正方形的可以被刻在里面的一边。 例:

Input: a = 5 
Output: 2.32

Input: a = 7
Output: 3.248

接近:让正方形的一边为 x 。 现在， AH 垂直于 DE 。 DE 与 BC 平行，所以，角度 AED =角度 ACB = 60

In triangle EFC,
              => Sin60 = x/ EC
              => √3 / 2 = x/EC
              => EC = 2x/√3
In triangle AHE,
              => Cos 60 = x/2AE
              => 1/2 = x/2AE
              => AE = x

所以，三角形的边AC=2x/√3+x。现在， a = 2x/√3 + x 因此， x = a/(1 + 2/√3) = 0.464a 以下是上述做法的实施:

C++

// C++ Program to find the biggest square
// which can be inscribed within the equilateral triangle
#include <bits/stdc++.h>
using namespace std;

// Function to find the side
// of the square
float square(float a)
{

    // the side cannot be negative
    if (a < 0)
        return -1;

    // side of the square
    float x = 0.464 * a;

    return x;
}

// Driver code
int main()
{
    float a = 5;
    cout << square(a) << endl;

    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java Program to find the
// the biggest square which
// can be inscribed within
// the equilateral triangle

class GFG
{
    // Function to find the side
    // of the square
    static double square(double a)
    {

        // the side cannot be negative
        if (a < 0)
            return -1;

        // side of the square
        double x = 0.464 * a;
        return x;
    }

    // Driver code
    public static void main(String []args)
    {
        double a = 5;
        System.out.println(square(a));
    }
}

// This code is contributed by ihritik

Python 3

# Python3 Program to find the biggest square
# which can be inscribed within the equilateral triangle

# Function to find the side
# of the square
def square( a ):

    # the side cannot be negative
    if (a < 0):
        return -1

    # side of the square
    x = 0.464 * a

    return x

# Driver code
a = 5
print(square(a))

# This code is contributed by ihritik

C

// C# Program to find the biggest
// square which can be inscribed
// within the equilateral triangle
using System;

class GFG
{
    // Function to find the side
    // of the square
    static double square(double a)
    {

        // the side cannot be negative
        if (a < 0)
            return -1;

        // side of the square
        double x = 0.464 * a;
        return x;
    }

    // Driver code
    public static void Main()
    {
        double a = 5;
        Console.WriteLine(square(a));
    }
}

// This code is contributed by ihritik

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP Program to find the biggest
//  square which can be inscribed
// within the equilateral triangle

// Function to find the side
// of the square
function square($a )
{

    // the side cannot be negative
    if ($a < 0)
        return -1;

    // side of the square
    $x = 0.464 * $a;
    return $x;
}

// Driver code
$a = 5;
echo square($a);

// This code is contributed by ihritik

?>

java 描述语言

<script>
// javascript Program to find the
// the biggest square which
// can be inscribed within
// the equilateral triangle

// Function to find the side
// of the square
function square(a)
{

    // the side cannot be negative
    if (a < 0)
        return -1;

    // side of the square
    var x = 0.464 * a;
    return x;
}

// Driver code
    var a = 5;
    document.write(square(a).toFixed(2));

// This code contributed by Princi Singh

</script>

Output: 

2.32

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