9. A company is required to fence off a square/rectangular area around a robot arm to comply with health and safety law. They have $750 \mathrm{~m}$ of fencing available. The task is to: a) Find the maximum square/rectangular area they can fence off?

Step 1 ：Let x be the length of one side of the rectangle and y be the length of the other side. The perimeter of the rectangle is given by the formula: \(\text{Perimeter} = 2x + 2y\)

Step 2 ：We know that the company has 750 meters of fencing available, so: \(750 = 2x + 2y\)

Step 3 ：Solve for y in the perimeter equation and substitute it into the area equation to get a single-variable equation: \(y = (750 - 2x) / 2\)

Step 4 ：Area of the rectangle is given by the formula: \(\text{Area} = x * y\)

Step 5 ：Substitute the value of y: \(\text{Area} = x * ((750 - 2x) / 2)\)

Step 6 ：Find the critical points of the area function and check the endpoints: \(\frac{d(\text{Area})}{dx} = 375 - 2x\)

Step 7 ：Critical point: \(x = \frac{375}{2}\)

Step 8 ：Calculate the maximum area: \(\text{Max Area} = \frac{140625}{4}\)

Step 9 ：\(\boxed{\text{Final Answer: The maximum square/rectangular area they can fence off is } \frac{140625}{4} \text{ square meters}}\)