Given a rectangle of length 
and breadth . The task is to find the area of the biggest triangle that can be inscribed in it.
Examples:
Input: L = 5, B = 4 Output: 10 Input: L = 3, B = 2 Output: 3
From the figure, it is clear that the largest triangle that can be inscribed in the rectangle, should stand on the same base & has height raising between the same parallel sides of the rectangle.
So, the base of the triangle = B
Height of the triangle = L
Therefore Area,
A = (L*B)/2
Note: It should also be clear that if base of the triangle = diagonal of rectangle, still the area of triangle so obtained = lb/2 as diagonal of a rectangle divides it into 2 triangles of equal area.
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest triangle// which can be inscribed within the rectangle#include <bits/stdc++.h>using namespace std;// Function to find the area// of the trianglefloat trianglearea(float l, float b){ // a and b cannot be negative if (l < 0 || b < 0) return -1; // area of the triangle float area = (l * b) / 2; return area;}// Driver codeint main(){ float l = 5, b = 4; cout << trianglearea(l, b) << endl; return 0;} |
Java
// Java Program to find the biggest triangle// which can be inscribed within the rectangleimport java.util.*;class GFG{ // Function to find the area // of the triangle static float trianglearea(float l, float b) { // a and b cannot be negative if (l < 0 || b < 0) return -1; // area of the triangle float area = (l * b) / 2; return area; } // Driver code public static void main(String args[]) { float l = 5, b = 4; System.out.println(trianglearea(l, b)); }} |
Python3
# Python3 Program to find the # biggest triangle which can be # inscribed within the rectangle # Function to find the area # of the triangle def trianglearea(l, b) : # a and b cannot be negative if (l < 0 or b < 0) : return -1 # area of the triangle area = (l * b) / 2 return area# Driver code l = 5b = 4print(trianglearea(l, b))# This code is contributed # by Yatin Gupta |
C#
// C# Program to find the biggest // triangle which can be inscribed// within the rectangleusing System;class GFG{// Function to find the area// of the trianglestatic float trianglearea(float l, float b){ // a and b cannot be negative if (l < 0 || b < 0) return -1; // area of the triangle float area = (l * b) / 2; return area;}// Driver codepublic static void Main(){ float l = 5, b = 4; Console.WriteLine(trianglearea(l, b));}}// This code is contributed // by inder_verma |
PHP
<?php// PHP Program to find the biggest // triangle which can be inscribed// within the rectangle// Function to find the area// of the trianglefunction trianglearea($l, $b){ // a and b cannot be negative if ($l < 0 or $b < 0) return -1; // area of the triangle $area = ($l * $b) / 2; return $area;}// Driver code$l = 5; $b = 4;echo trianglearea($l, $b);// This code is contributed // by inder_verma?> |
Javascript
<script>// javascript Program to find the biggest triangle// which can be inscribed within the rectangle// Function to find the area// of the trianglefunction trianglearea( l, b){ // a and b cannot be negative if (l < 0 || b < 0) return -1; // area of the triangle let area = (l * b) / 2; return area;}// Driver code let l = 5, b = 4; document.write( trianglearea(l, b) );// This code contributed by aashish1995 </script> |
10
Time Complexity: O(1) since performing constant operations
Auxiliary Space: O(1), since no extra space has been taken.
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