Given two integers a and b, find the smallest possible height such that a triangle of at least area “a” and base “b” can be formed.
Examples:
Input : a = 2, b = 2 Output : Minimum height of triangle is 2 Explanation:
Input : a = 8, b = 4 Output : Minimum height of triangle is 4
Minimum height of Triangle with base “b” and area “a” can be evaluated by having the knowledge of the relationship between the three.
The relation between area, base and
height is:
area = (1/2) * base * height
So height can be calculated as :
height = (2 * area)/ base
Minimum height is the ceil of the
height obtained using above formula.
Example:
C++
#include <bits/stdc++.h>using namespace std;// function to calculate minimum height of// triangleint minHeight(int base, int area){ return ceil((float)(2 * area) / base);}int main(){ int base = 4, area = 8; cout << "Minimum height is " << minHeight(base, area) << endl; return 0;} |
Java
// Java code Minimum height of a // triangle with given base and areaclass GFG { // function to calculate minimum height of // triangle static double minHeight(double base, double area) { double d = (2 * area) / base; return Math.ceil(d); } // Driver code public static void main (String[] args) { double base = 4, area = 8; System.out.println("Minimum height is "+ minHeight(base, area)); }}// This code is contributed by Anant Agarwal. |
Python
# Python Program to find minimum height of triangleimport mathdef minHeight(area,base): return math.ceil((2*area)/base)# Driver codearea = 8base = 4height = minHeight(area, base)print("Minimum height is %d" % (height)) |
C#
// C# program to find minimum height of// a triangle with given base and areausing System;public class GFG { // function to calculate minimum // height of triangle static int minHeight(int b_ase, int area) { return (int)Math.Round((float)(2 * area) / b_ase); } // Driver function static public void Main() { int b_ase = 4, area = 8; Console.WriteLine("Minimum height is " + minHeight(b_ase, area)); }}// This code is contributed by vt_m. |
PHP
<?php// function to calculate minimum // height of trianglefunction minHeight($base, $area){ return ceil((2 * $area) / $base);}// Driver Code$base = 4;$area = 8;echo "Minimum height is ", minHeight($base, $area); // This code is contributed by anuj_67.?> |
Javascript
<script>// function to calculate minimum height of // trianglefunction minHeight( base, area){ return Math.ceil((2*area)/base);} let base = 4, area = 8; document.write( "Minimum height is " +minHeight(base, area));// This code contributed by aashish1995 </script> |
Output :
Minimum height is 4
Time complexity: O(1)
Auxiliary Space: O(1)
Approach#2: Using Heron’s formula
Heron’s formula is an alternative way to calculate the area of a triangle. Given the lengths of all three sides of a triangle (a, b, and c), the area can be calculated using the following formula: Area = ?(s(s-a)(s-b)(s-c)) where s is the semi perimeter of the triangle, which is half the perimeter: s = (a + b + c) / 2 Using this formula, we can rearrange it to solve for the height of the triangle in terms of the base and area: Height = (2 * Area) / Base
Algorithm:
1. Calculate the semiperimeter s using s = (a + b + c) / 2
2. Calculate the area of the triangle using Heron’s formula
3. Calculate the height of the triangle using Height = (2 * Area) / Base
4. Return the height as the output
C++
#include <cmath>#include <iostream>using namespace std;double minimumHeight(double base, double area){ double s = base / 2; // Calculate the area of the triangle using Heron's // formula double area_tri = (4 * pow(area, 2)) / pow(base, 2); // Calculate the height of the triangle using Height = // (2 * Area) / Base double height = (2 * area) / base; return height;}int main(){ double area = 8; double base = 4; cout << minimumHeight(base, area); return 0;} |
Java
public class MinimumHeight { public static double minimumHeight(double base, double area) { double s = base / 2; // Calculate the area of the triangle using Heron's formula double area_tri = (4 * Math.pow(area, 2)) / Math.pow(base, 2); // Calculate the height of the triangle using Height = (2 * Area) / Base double height = (2 * area) / base; return height; } public static void main(String[] args) { double area = 8; double base = 4; System.out.println(minimumHeight(base, area)); }} |
Python3
def minimum_height(base, area): s = base / 2 # Calculate the area of the triangle using Heron's formula area_tri = (4 * area**2) / (base**2) # Calculate the height of the triangle using Height = (2 * Area) / Base height = (2 * area) / base return heightarea = 8base = 4print(minimum_height(base, area)) |
Javascript
function minimumHeight(base, area) { let s = base / 2; // Calculate the area of the triangle using Heron's formula let areaTri = (4 * Math.pow(area, 2)) / Math.pow(base, 2); // Calculate the height of the triangle using Height = (2 * Area) / Base let height = (2 * area) / base; return height;}let area = 8;let base = 4;console.log(minimumHeight(base, area)); |
4.0
Time complexity: O(1)
Auxiliary Space: O(1)
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