**Explanation:**

In a flange coupling, the flanges are the outer circular plates that are used to connect two shafts together. The flanges are typically made of steel or cast iron and are designed to be strong and rigid in order to transmit the torque from one shaft to another.

The thickness of the flanges is an important parameter in the design of a flange coupling. It determines the strength and rigidity of the coupling, as well as the amount of torque that can be transmitted.

The statement in the question, that the thickness of the flanges is taken as one-half the diameter of the shaft, is correct and is commonly used in the design of flange couplings.

**Reasons for the Correct Answer:**

1. **Strength and Rigidity:** The thickness of the flanges is directly related to the strength and rigidity of the coupling. A thicker flange will be stronger and more rigid, which will allow it to transmit higher torques without failure. Therefore, taking the thickness as one-half the diameter of the shaft ensures sufficient strength and rigidity for most applications.

2. **Torque Transmission:** The thickness of the flanges also affects the amount of torque that can be transmitted through the coupling. A thicker flange will have a larger contact area with the shaft, which will allow it to transmit higher torques. By taking the thickness as one-half the diameter of the shaft, the contact area is maximized, resulting in increased torque transmission capability.

3. **Manufacturing Considerations:** Taking the thickness of the flanges as one-half the diameter of the shaft also simplifies the manufacturing process. It allows for easier machining and fabrication of the flanges, as the dimensions are directly related to the shaft diameter.

4. **Industry Standard:** The practice of taking the thickness of the flanges as one-half the diameter of the shaft is widely accepted and used in the industry. It is based on years of experience and empirical data, and has been proven to provide reliable and efficient coupling designs.

Therefore, the correct answer to the question is option 'A' (Agree). Taking the thickness of the flanges as one-half the diameter of the shaft is a common practice in the design of flange couplings, and it ensures sufficient strength, rigidity, and torque transmission capability.