A farmer has 100 m of fencing to make a rectangular pen with 3 congruent rectangular subdivision side by side. Each subdivisions must be 3 meter wide and at least 8 meters long. What is the range of the possible length of it's division?
so, if the divisions are x meters long, we have
4*3 + 6x <= 100
6x <= 88
x <= 44/3
so,
8 <= x <= 44/3
To find the range of possible lengths for the subdivisions, we need to consider the given constraints and make an equation to solve for the possible values.
Let's assume the length of each subdivision is x meters.
The width of each subdivision is given as 3 meters, and we need 3 subdivisions side by side. So, the total width of the pen would be 3 * 3 = 9 meters.
The total length of the pen would be 3 times the length of each subdivision, so it becomes 3x.
Now, we can create an equation using the perimeter of the pen:
Perimeter = Total Length + Total Width + Total Length + Total Width
From the given information, we know that the total perimeter of the pen is 100 meters:
100 = 3x + 9 + 3x + 9
Simplifying the equation:
100 = 6x + 18
Subtracting 18 from both sides:
82 = 6x
Dividing both sides by 6:
x = 13.67
Since the length of the subdivision must be at least 8 meters, the range of possible lengths for the divisions is 8 ≤ x ≤ 13.67.
Therefore, the range of possible lengths for the subdivisions is 8 to 13.67 meters.