Why is the RMS of sinusoidal alternating current equal to twice the root of the peak?

Why is the RMS of sinusoidal alternating current equal to twice the root of the peak?

Average power = work / time
Work is the area under the sine curve (which can be obtained by integration), and time is the abscissa
According to the above calculation, the average power of sinusoidal alternating current is 1 / √ 2 times of the peak value
The effective current is proportional to the average power