Why Peak-to-peak voltage is twice the peak, so 200 V p-p is 100 V peak. For a sine wave the RMS value is 0.707 times the peak, giving 70.7 V RMS. Power into a resistive load is V(RMS) squared divided by R: 70.7 squared is about 5000, divided by 50 ohms gives 100 watts. PEP into a dummy load with a steady sine wave is simply this average power.
Watch out The 400 watt choice comes from using the full 200 V peak-to-peak as if it were RMS, and 353.5 watts comes from squaring 100 V peak without converting to RMS first (and mixing up the arithmetic); both skip one of the two required conversions.
Two steps: halve p-p to get peak, times 0.707 for RMS, then V(RMS)^2/R. 200 p-p into 50 ohms = 100 W.