# Minimum height of a triangle with given base and area

• Difficulty Level : Basic
• Last Updated : 16 Jun, 2022

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 ``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

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## Javascript

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Output :

`Minimum height is 4`

Time complexity: O(1)
Auxiliary Space: O(1)

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