# 492. Construct the Rectangle

## Description

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

## Solutions

• class Solution {
public int[] constructRectangle(int area) {
int w = (int) Math.sqrt(area);
while (area % w != 0) {
--w;
}
return new int[] {area / w, w};
}
}

• class Solution {
public:
vector<int> constructRectangle(int area) {
int w = sqrt(1.0 * area);
while (area % w != 0) --w;
return {area / w, w};
}
};

• class Solution:
def constructRectangle(self, area: int) -> List[int]:
w = int(sqrt(area))
while area % w != 0:
w -= 1
return [area // w, w]


• func constructRectangle(area int) []int {
w := int(math.Sqrt(float64(area)))
for area%w != 0 {
w--
}
return []int{area / w, w}
}