### Instruction: A rectangle having integer length and width has a perimeter of 100 units. What is the number of square units in the least possible area?### Response: I know that the perimeter of a rectangle is the sum of the lengths of all four sides, so if I let x be the length and y be the width, I have 2x + 2y = 100.
I can simplify this equation by dividing both sides by 2, giving me x + y = 50.
Now, I want to minimize the area of the rectangle, which is xy.
I recall that for a fixed sum, the product of two numbers is maximized when they are equal, and minimized when they are as far apart as possible.
So, to minimize xy, I want to make x and y as far apart as possible, subject to the constraint that they are positive integers and their sum is 50.
The farthest apart they can be is when one of them is 1 and the other is 49, since 1 + 49 = 50.