Given:
- In the adjoining figure, pqrs is a rectangle.
- op = (2x-3) cm
- or = (x+1) cm

To find:
The length of diagonal qs.

Explanation:
We know that in a rectangle, opposite sides are equal in length. Therefore, pq = rs and qs = pr.

Let's find the values of pq and pr using the given information.

Finding pq:
Given that op = (2x-3) cm and or = (x+1) cm.

Since pq = rs, we can equate their lengths:
2x - 3 = x + 1

Simplifying the equation:
2x - x = 1 + 3
x = 4

Therefore, pq = rs = 2x - 3 = 2(4) - 3 = 8 - 3 = 5 cm.

Finding qs:
Since qs = pr, we need to find the length of pr.

We can use the Pythagorean theorem to find pr. According to the theorem, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In triangle opr,
op^2 + or^2 = pr^2

Substituting the given values:
(2x-3)^2 + (x+1)^2 = pr^2

Expanding and simplifying the equation:
4x^2 - 12x + 9 + x^2 + 2x + 1 = pr^2
5x^2 - 10x + 10 = pr^2

Since pr = qs, we can write:
5x^2 - 10x + 10 = qs^2

Key Points:
- In a rectangle, opposite sides are equal in length.
- The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Finding the length of qs:
To find the length of qs, we need to find the value of qs^2 from the equation 5x^2 - 10x + 10 = qs^2.

Since we don't have any additional information or constraints, we cannot determine the exact length of qs without solving the quadratic equation.

Conclusion:
In the given figure, pqrs is a rectangle. The length of the diagonal qs can be determined by finding the values of pq and pr using the given information. However, without solving the quadratic equation, we cannot determine the exact length of qs.