Minimum height of a triangle with given base and area

Last Updated : 16 Mar, 2021

Given two integers a and b, find the smallest possible height such that a triangle of atleast 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.

C++

#include <bits/stdc++.h>
using namespace std;
// function to calculate minimum height of
// triangle
int 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 area
 
class 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 triangle
import math
 
def minHeight(area,base):
        return math.ceil((2*area)/base)
 
# Driver code
area = 8
base = 4
height = minHeight(area, base)
print("Minimum height is %d" % (height))

C#

// C# program to find minimum height of
// a triangle with given base and area
using 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 triangle
function 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
// triangle
function 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

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