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

Answer 1

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