Given here is a right angle triangle with height l, base b & hypotenuse h, which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.
Examples:
Input: l = 5, b = 12, h = 13 Output: 8.77914 Input: l = 3, b = 4, h = 5 Output: 2.07116
Approach: We know, the side of the square inscribed within a right angled triangle is, a = (l*b)/(l+b), please refer Area of a largest square fit in a right angle triangle.
Also, in the reuleaux triangle, x = a.
So, x = (l*b)/(l+b).
So, Area of the Reuleaux Triangle is, A = 0.70477*x^2 = 0.70477*((l*b)/(l+b))^2.
Below is the implementation of the above approach:
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 trianglefloat 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 codeint 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 circleimport java.util.*;import java.text.DecimalFormat;class GFG{// Function to find the biggest reuleaux trianglestatic 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 codepublic 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 circleimport math as mt # Function to find the biggest # reuleaux triangledef 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 codel, b, h = 5, 12, 13print(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 circleusing System;class GFG{// Function to find the biggest reuleaux trianglestatic 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 codepublic static void Main(){ double l = 5, b = 12, h = 13; Console.WriteLine((Area(l, b, h)));}}// This code is contributed by// Mukul Singh |
PHP
<?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 trianglefunction 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?> |
Javascript
<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 trianglefunction 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 codelet l = 5, b = 12, h = 13; document.write( Area(l,b,h).toFixed(5));// This code contributed by Rajput-Ji </script> |
Output:
8.77914
Time Complexity: O(1)
Auxiliary Space: O(1)
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