Jim wants to fence a rectangular pen for his chickens. The length of the pen should be at 78 feet and the perimeter should be no more than 412 feet. Which system of inequalities represent the possible dimensions of the pen?(1 point) Responses
Let's assume the width of the pen is represented by x.
The length of the pen is given as 78 feet, so we have the equation:
Length = 78
The perimeter of a rectangle can be calculated using the formula:
Perimeter = 2 * (Length + Width)
In this case, the perimeter should be no more than 412 feet. So we have the inequality:
2 * (78 + x) ≤ 412
Simplifying this inequality, we get:
156 + 2x ≤ 412
Subtracting 156 from both sides, we have:
2x ≤ 256
Dividing both sides by 2, we get:
x ≤ 128
Therefore, the system of inequalities representing the possible dimensions of the pen is:
Length = 78
Width ≤ 128