# Construct The Rectangle Problem

## Description

LeetCode Problem 492.

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:

- The area of the rectangular web page you designed must equal to the given target area.
- The width W should not be larger than the length L, which means L >= W.
- 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 theweb page you designed in sequence.

Example 1:

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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:

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

Example 3:

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

Constraints:

- 1 <= area <= 10^7

## Sample C++ Code

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class Solution {
public:
vector<int> constructRectangle(int area) {
// The width is always less than or equal to the square root of the area,
// so we start searching from sqrt(area) until we find the result.
int a = sqrt(area);
while (area % a) {
a--;
}
return {area / a, a};
}
};