Find the length and width of a rectangle that has a perimeter of 100 meters and a maximum area

A rectangle with maximum area is always a square

a square has the same length and width.

to find the length of the side of a square with the known area, you would take the square root of the area

so in this case, the side length = square root of 100

square root (100) = 10 (check: 10 x 10 = 100)

so both the length and the width equal 10 meters