# Minimum height of a triangle with given base and area

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

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