Let's denote the width of the rectangle as 'w'.
According to the problem statement, the length of the rectangle is 2.25 meters greater than the width. Therefore, the length of the rectangle can be expressed as 'w + 2.25'.
The area of the court is the sum of the area of the rectangle and the area of the semi-circle on top.
The area of the rectangle is given by the formula: length * width.
So, the area of the rectangle is: (w + 2.25) * w.
The area of a semi-circle is given by the formula: (1/2) * pi * radius^2.
In this case, the radius of the semi-circle is equal to half of the width of the rectangle. So, the radius is: w / 2.
The area of the semi-circle is: (1/2) * 3.14 * (w / 2)^2.
The total area of the court is given to be 31.28 square meters. Therefore, we have the equation:
(w + 2.25) * w + (1/2) * 3.14 * (w / 2)^2 = 31.28.
Now, we can solve this equation to find the value of 'w'.