Area of a rectangle is Length x Width. So a rectangle that is 15ft x 12ft = 180ft. If the second rectangular room has an area that is one half the size that mean the area of the second room must be half of 180.
180 / 2 = 90. The second room can have any dimensions as long as they multiply together to get 90. One example would be 10ft by 9ft room.
for part B: it seems that a room with smaller area has smaller dimensions.