Area of a largest square fit in a right angle triangle
Given a right angled triangle with height l, base b & hypotenuse h.We need to find the area of the largest square that can fit in the right angled triangle.
Examples:
Input: l = 3, b = 4, h = 5 Output: 2.93878 The biggest square that can fit inside is of 1.71428 * 1.71428 dimension Input: l = 5, b = 12, h = 13 Output: 12.4567
Considering the above diagram, we see,tanx = l/b.
Here it is also true that, tanx = a/(b-a).
So, l/b = a/(b-a) which means that, a = (l*b)/(l+b)
Below is the required implementation:
C++
// C++ Program to find the area of the biggest square // which can fit inside the right angled traingle #include <bits/stdc++.h> using namespace std; // Function to find the area of the biggest square float squareArea(float l, float b, float h) { // the height or base or hypotenuse // cannot be negative if (l < 0 || b < 0 || h < 0) return -1; // side of the square float a = (l * b) / (l + b); // squaring to get the area return a * a; } // Driver code int main() { float l = 5, b = 12, h = 13; cout << squareArea(l, b, h) << endl; return 0; } |
Java
//Java Program to find the area of the biggest square //which can fit inside the right angled traingle public class GFG { //Function to find the area of the biggest square static float squareArea(float l, float b, float h) { // the height or base or hypotenuse // cannot be negative if (l < 0 || b < 0 || h < 0) return -1; // side of the square float a = (l * b) / (l + b); // squaring to get the area return a * a; } //Driver code public static void main(String[] args) { float l = 5, b = 12, h = 13; System.out.println(squareArea(l, b, h)); } } |
Python 3
# Python 3 Program to find the # area of the biggest square # which can fit inside the right # angled traingle # Function to find the area of the biggest square def squareArea(l, b, h) : # the height or base or hypotenuse # cannot be negative if l < 0 or b < 0 or h < 0 : return -1 # side of the square a = (l * b) / (l + b) # squaring to get the area return a * a # Driver Code if __name__ == "__main__" : l, b, h = 5, 12, 13 print(round(squareArea(l, b, h),4)) # This code is contributed by ANKITRAI1 |
C#
// C# Program to find the area of // the biggest square which can // fit inside the right angled triangle using System; class GFG { // Function to find the area // of the biggest square static float squareArea(float l, float b, float h) { // the height or base or hypotenuse // cannot be negative if (l < 0 || b < 0 || h < 0) return -1; // side of the square float a = (l * b) / (l + b); // squaring to get the area return a * a; } // Driver code public static void Main() { float l = 5, b = 12, h = 13; Console.WriteLine(squareArea(l, b, h)); } } // This code is contributed // by inder_verma.. |
PHP
<?php // PHP Program to find the area // of the biggest square which // can fit inside the right // angled triangle // Function to find the area // of the biggest square function squareArea($l, $b, $h) { // the height or base or // hypotenuse cannot be // negative if ($l < 0 || $b < 0 || $h < 0) return -1; // side of the square $a = ($l * $b) / ($l + $b); // squaring to get the area return $a * $a; } // Driver code $l = 5; $b = 12; $h = 13; echo round(squareArea($l, $b, $h), 4); // This code is contributed by mits ?> |
Output:
12.4567
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