Answer:
40 ft by 70 ft
Step-by-step explanation:
The 50 ft side of the house can add to the total perimeter of the play area, allowing it to be 170+50 = 220 feet. Then the sum of length and width will be half that, or 110 feet.
Factors of 2800 that have a sum of 110 are 40 and 70.
The play area fence can extend 10 ft either side of the house, out 40 ft, then 70 ft across the back, for a total length of 170 ft. Dimensions of the play area are 40 ft by 70 ft.