The correct answer is A. Square root of the discharge.
The length and width of a meander and also the width of the river, vary roughly as the square root of the discharge. This is because the discharge is a measure of the amount of water flowing in the river, and the more water that flows, the more energy the river has to erode the banks and create meanders.
The square root of the discharge is used because it is a measure of the average velocity of the water. The average velocity is important because it is a measure of the amount of energy that the river has to erode the banks.
The other options are incorrect because they do not take into account the average velocity of the water. The discharge is a measure of the total amount of water flowing in the river, but it does not take into account how fast the water is flowing. The square of the discharge and the cube of the discharge are even less accurate because they do not take into account the average velocity of the water at all.