A) 5000 m² b) A(x) = x(200 -2x) c) 0 < x < 100 Step-by-step explanation: b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground: A(x) = x(200 -2x) __ a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m² __ c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.
