A rectangular region, placed against a wall of a house, is divided into three equal regions using a total of 120 meters of fencing. Calculate the maximum area possible for the entire region.
What is the length?
Let x be the length of the rectangular region. Since the region is divided into three equal parts, each part will have a length of x/3.
The perimeter of the rectangular region can be calculated as:
2x + 2(x/3) = 120
2x + 2x/3 = 120
6x + 2x = 360
8x = 360
x = 45
So, the length of the rectangular region is 45 meters.
The maximum area of the entire region can be calculated as:
Area = (length)(width)
Area = 45(3)(45)
Area = 2025 square meters
Therefore, the maximum area possible for the entire region is 2025 square meters.