Given:
The figure RENT is a rectangle.
The diagonals of the rectangle meet at point O.
OR = 2x + 4
OT = 3x + 1

To find:
The value of x.

Explanation:
Step 1: Understanding the properties of a rectangle
A rectangle is a quadrilateral with four right angles. It has two pairs of opposite sides that are congruent and parallel. The diagonals of a rectangle are equal in length and bisect each other.

Step 2: Identifying the given information
In the given figure, we know that the diagonals of the rectangle meet at point O. We are given the lengths of two segments of the diagonals:
- OR = 2x + 4
- OT = 3x + 1

Step 3: Using the properties of a rectangle
Since the diagonals of a rectangle bisect each other, we can conclude that point O is the midpoint of both diagonals. Therefore, we can set up an equation using the lengths of the segments on one diagonal and solve for x.

Step 4: Finding the value of x
Since O is the midpoint of OR, we can write:
OR = 2x + 4 = 2(OR/2) + 4

Simplifying the equation:
2x + 4 = OR + 4
2x = OR
x = OR/2

Similarly, since O is the midpoint of OT, we can write:
OT = 3x + 1 = 2(OT/2) + 1

Simplifying the equation:
3x + 1 = OT + 1
3x = OT
x = OT/3

Since both expressions for x are equal to the lengths of the diagonals divided by 2 and 3 respectively, we can conclude that:
OR/2 = OT/3

Step 5: Solving for x
Using the equation OR/2 = OT/3, we can substitute the given values:
(2x + 4)/2 = (3x + 1)/3

Cross-multiplying:
3(2x + 4) = 2(3x + 1)
6x + 12 = 6x + 2

Simplifying the equation:
12 - 2 = 6x - 6x
10 = 0 (This equation is inconsistent)

Conclusion:
The equation obtained in step 5 does not have a solution. Therefore, it is not possible to determine the value of x based on the given information.

Given, In a rectangle RENT : OR = (2x + 4) And, OT = (3x + 1) We know that the diagonals of a rectangle are equal Therefore, 2x + 4 = 3x + 1 = 2x - 3x = 1 - 4 = x = 3 So, OR = 2 × 3 + 4 = 10 OT = 3 × 3 + 1 = 10