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 the length of the rectangular region be x meters. Since the region is divided into three equal parts, each part will have a width of x/3 meters.
The total fencing used is given by:
2x + 4(x/3) = 120
2x + 4x/3 = 120
6x + 4x = 360
10x = 360
x = 36
Therefore, the length of the rectangular region is 36 meters.
The maximum area of the entire region can be calculated by finding the area of one part and then multiplying it by 3.
Area of one part = x * (x/3) = 36 * (36/3) = 36 * 12 = 432 square meters
Therefore, the maximum area possible for the entire region is 432 * 3 = 1296 square meters.