## Algorithm

Problem Name: 492. Construct the Rectangle

A web developer needs to know how to design a web page's size. So, given a specific rectangular web page’s area, your job by now is to design a rectangular web page, whose length L and width W satisfy the following requirements:

1. The area of the rectangular web page you designed must equal to the given target area.
2. The width `W` should not be larger than the length `L`, which means `L >= W`.
3. The difference between length `L` and width `W` should be as small as possible.

Return an array `[L, W]` where `L` and `W` are the length and width of the web page you designed in sequence.

Example 1:

```Input: area = 4
Output: [2,2]
Explanation: The target area is 4, and all the possible ways to construct it are [1,4], [2,2], [4,1].
But according to requirement 2, [1,4] is illegal; according to requirement 3,  [4,1] is not optimal compared to [2,2]. So the length L is 2, and the width W is 2.
```

Example 2:

```Input: area = 37
Output: [37,1]
```

Example 3:

```Input: area = 122122
Output: [427,286]
```

Constraints:

• `1 <= area <= 107`

## Code Examples

### #1 Code Example with Java Programming

```Code - Java Programming```

``````
class Solution {
public int[] constructRectangle(int area) {
int[] ans = new int[2];

if(area == 0){
return ans;
}

int a = (int)Math.sqrt(area);
while(area%a != 0) {
a--;
}

int b = area/a;
ans[0] = b;
ans[1] = a;

return ans;
}
}
``````
Copy The Code &

Input

cmd
area = 4

Output

cmd
[2,2]

### #2 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const constructRectangle = function(area) {
let w = Math.sqrt(area) >> 0;
while (area % w != 0) w--;
return [(area / w) >> 0, w];
};
``````
Copy The Code &

Input

cmd
area = 4

Output

cmd
[2,2]

### #3 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def constructRectangle(self, area):
"""
:type area: int
:rtype: List[int]
"""
import math
l, w = int(math.sqrt(area)), int(math.sqrt(area))
while l*w!=area:
if area%w==0: l=int(area/w)
else: w-=1
return [l,w]
``````
Copy The Code &

Input

cmd
area = 37

Output

cmd
[37,1]

### #4 Code Example with C# Programming

```Code - C# Programming```

``````
using System;

namespace LeetCode
{
public class _0492_ConstructTheRectangle
{
public int[] ConstructRectangle(int area)
{
var w = (int)Math.Sqrt(area);
while (area % w != 0) w--;
return new int[] { area / w, w };
}
}
}
``````
Copy The Code &

Input

cmd
area = 37

Output

cmd
[37,1]