直角三角形内接的正方形内最大的三角形
这里给出的是一个直角三角形，其高度为 l ，底边为 b &斜边为 h ，上面刻有一个正方形，正方形又刻有一个三角形。任务是找到这个 reuleaux 三角形的最大可能面积。 举例:
Input: l = 5, b = 12, h = 13
Output: 8.77914
Input: l = 3, b = 4, h = 5
Output: 2.07116
逼近:我们知道，直角三角形内接正方形的边是， a = (l*b)/(l+b) ，请参考直角三角形内最大正方形的面积拟合。 同样，在 reuleaux 三角形中， x = a 。 所以， x = (l*b)/(l+b) 。 所以，勒鲁三角的面积为，a = 0.70477x^2 = 0.70477((l*b)/(l+b))^2。 以下是上述方法的实施:
C++
// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a circle
#include <bits/stdc++.h>
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 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP 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 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 = 5; $b = 12; $h = 13;
echo Area($l, $b, $h);
// This code is contributed by
// anuj_67
?>
java 描述语言
<script>
// 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
</script>
Output:
8.77914
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