直角三角形内刻有正方形的最大Reuleaux三角形

此处给出的是一个高度为l ，底边为b且斜边为h的直角三角形，该三角形内接一个正方形，该方形又接一个reuleaux三角形。任务是找到该reuleaux三角形的最大可能面积。
例子：

Input: l = 5, b = 12, h = 13
Output: 8.77914

Input: l = 3, b = 4, h = 5
Output: 2.07116

方法：我们知道，直角三角形内的正方形的边为a =(l * b)/(l + b) ，请参考直角三角形中最大的正方形拟合的面积。
另外，在鲁洛三角形中， x = a 。
因此， x =(l * b)/(l + b) 。
因此，Reuleaux三角形的面积为，A = 0.70477 * x ^ 2 = 0.70477 *((l * b)/(l + b))^ 2 。
下面是上述方法的实现：

C++

// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a circle
#include 
using namespace std;
 
// Function to find the biggest reuleaux triangle
float Area(float l, float b, float h)
{
 
    // the height or base or hypotenuse
    // cannot be negative
    if (l < 0 || b < 0 || h < 0)
        return -1;
 
    // height of the reuleaux triangle
    float x = (l * b) / (l + b);
 
    // area of the reuleaux triangle
    float A = 0.70477 * pow(x, 2);
 
    return A;
}
 
// Driver code
int main()
{
    float l = 5, b = 12, h = 13;
    cout << Area(l, b, h) << endl;
 
    return 0;
}

Java

// Java Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a circle
import java.util.*;
import java.text.DecimalFormat;
 
class GFG
{
 
// Function to find the biggest reuleaux triangle
static double Area(double l, double b, double h)
{
 
    // the height or base or hypotenuse
    // cannot be negative
    if (l < 0 || b < 0 || h < 0)
        return -1;
 
    // height of the reuleaux triangle
    double x = (l * b) / (l + b);
 
    // area of the reuleaux triangle
    double A = 0.70477 * Math.pow(x, 2);
 
    return A;
}
 
// Driver code
public static void main(String args[])
{
    double l = 5, b = 12, h = 13;
    DecimalFormat df = new DecimalFormat("#,###,##0.00000");
    System.out.println(df.format(Area(l, b, h)));
}
}
 
// This code is contributed by
// Shashank_Sharma

Python3

# Python3 Program to find the biggest
# Reuleaux triangle inscribed within
# in a square which in turn is inscribed
# within a circle
import math as mt
 
# Function to find the biggest
# reuleaux triangle
def Area(l, b, h):
 
    # the height or base or hypotenuse
    # cannot be negative
    if (l < 0 or b < 0 or h < 0):
        return -1
 
    # height of the reuleaux triangle
    x = (l * b) /(l + b)
 
    # area of the reuleaux triangle
    A = 0.70477 * pow(x, 2)
 
    return A
 
# Driver code
l, b, h = 5, 12, 13
print(Area(l, b, h))
 
# This code is contributed by
# Mohit kumar 29

C#

// C# Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a circle
using System;
 
class GFG
{
 
// Function to find the biggest reuleaux triangle
static double Area(double l, double b, double h)
{
 
    // the height or base or hypotenuse
    // cannot be negative
    if (l < 0 || b < 0 || h < 0)
        return -1;
 
    // height of the reuleaux triangle
    double x = (l * b) / (l + b);
 
    // area of the reuleaux triangle
    double A = 0.70477 * Math.Pow(x, 2);
 
    return A;
}
 
// Driver code
public static void Main()
{
    double l = 5, b = 12, h = 13;
    Console.WriteLine((Area(l, b, h)));
}
}
 
// This code is contributed by
// Mukul Singh

Javascript

 
// Javascript Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a circle
 
 
// Function to find the biggest reuleaux triangle
function Area(l,b,h)
{
 
    // the height or base or hypotenuse
    // cannot be negative
    if (l < 0 || b < 0 || h < 0)
        return -1;
 
    // height of the reuleaux triangle
    let x = (l * b) / (l + b);
 
    // area of the reuleaux triangle
    let A = 0.70477 * Math.pow(x, 2);
 
    return A;
}
 
// Driver code
let l = 5, b = 12, h = 13;
  
    document.write( Area(l,b,h).toFixed(5));
 
// This code contributed by Rajput-Ji
 

输出：

8.77914