If the sides of the perimeter are integers, 1 is the minimum side length of any particular side. So, 49 would have to be the length of the adjacent side.....
Note 1 + 49 + 1 + 49 = 100 = the perimeter
So... the minimum square area would be (1) (49) = 49 square units...
Here's a graph of the situation with some of the integer possibilities......https://www.desmos.com/calculator/ap3s1jlsnv
Notice that after x = 1, the values of x from 2 to 25 inclusive all produce greater areas....!!!
If the sides of the perimeter are integers, 1 is the minimum side length of any particular side. So, 49 would have to be the length of the adjacent side.....
Note 1 + 49 + 1 + 49 = 100 = the perimeter
So... the minimum square area would be (1) (49) = 49 square units...
Here's a graph of the situation with some of the integer possibilities......https://www.desmos.com/calculator/ap3s1jlsnv
Notice that after x = 1, the values of x from 2 to 25 inclusive all produce greater areas....!!!