Let's say that each side of the garden is increased by x feet.
Original area = 25*50=1250 sq ft,
new area=1250+400=1650=(x+25)(x+50).
So x^2+75x+1250=1650; x^2+75x-400=0=(x-5)(x+80). So x=5 or -80. We reject -80 because we can't have a negative length, so the extension is 5 feet.
The new size of the garden is 30 by 55 and the area is 1650 sq feet, 400 sq ft more than before.