# 3000. Maximum Area of Longest Diagonal Rectangle

## Description

You are given a 2D 0-indexed integer array dimensions.

For all indices i, 0 <= i < dimensions.length, dimensions[i][0] represents the length and dimensions[i][1] represents the width of the rectangle i.

Return the area of the rectangle having the longest diagonal. If there are multiple rectangles with the longest diagonal, return the area of the rectangle having the maximum area.

Example 1:

Input: dimensions = [[9,3],[8,6]]
Output: 48
Explanation:
For index = 0, length = 9 and width = 3. Diagonal length = sqrt(9 * 9 + 3 * 3) = sqrt(90) ≈ 9.487.
For index = 1, length = 8 and width = 6. Diagonal length = sqrt(8 * 8 + 6 * 6) = sqrt(100) = 10.
So, the rectangle at index 1 has a greater diagonal length therefore we return area = 8 * 6 = 48.


Example 2:

Input: dimensions = [[3,4],[4,3]]
Output: 12
Explanation: Length of diagonal is the same for both which is 5, so maximum area = 12.


Constraints:

• 1 <= dimensions.length <= 100
• dimensions[i].length == 2
• 1 <= dimensions[i][0], dimensions[i][1] <= 100

## Solutions

• class Solution {
public int areaOfMaxDiagonal(int[][] dimensions) {
int ans = 0, mx = 0;
for (var d : dimensions) {
int l = d[0], w = d[1];
int t = l * l + w * w;
if (mx < t) {
mx = t;
ans = l * w;
} else if (mx == t) {
ans = Math.max(ans, l * w);
}
}
return ans;
}
}

• class Solution {
public:
int areaOfMaxDiagonal(vector<vector<int>>& dimensions) {
int ans = 0, mx = 0;
for (auto& d : dimensions) {
int l = d[0], w = d[1];
int t = l * l + w * w;
if (mx < t) {
mx = t;
ans = l * w;
} else if (mx == t) {
ans = max(ans, l * w);
}
}
return ans;
}
};

• class Solution:
def areaOfMaxDiagonal(self, dimensions: List[List[int]]) -> int:
ans = mx = 0
for l, w in dimensions:
t = l**2 + w**2
if mx < t:
mx = t
ans = l * w
elif mx == t:
ans = max(ans, l * w)
return ans


• func areaOfMaxDiagonal(dimensions [][]int) (ans int) {
mx := 0
for _, d := range dimensions {
l, w := d[0], d[1]
t := l*l + w*w
if mx < t {
mx = t
ans = l * w
} else if mx == t {
ans = max(ans, l*w)
}
}
return
}

• function areaOfMaxDiagonal(dimensions: number[][]): number {
let [ans, mx] = [0, 0];
for (const [l, w] of dimensions) {
const t = l * l + w * w;
if (mx < t) {
mx = t;
ans = l * w;
} else if (mx === t) {
ans = Math.max(ans, l * w);
}
}
return ans;
}