Final answer:
To fence in a rectangular playground using one of the walls of the building with 100ft of donated fencing, the dimensions of the playground should be 140ft by 100ft.
Step-by-step explanation:
To fence in a rectangular playground using one wall of the building, you need to consider that the donated fencing is 100ft long. Let's denote the width of the playground as w and the length as L.
The donated fencing will be used for three sides of the rectangular playground: two sides with the length L and one side with the width w. The sum of the lengths of these three sides should be equal to 100ft.
Therefore, we can write the equation as: 2L + w = 100.
Given that w = 100ft and L = 140ft, we can substitute these values into the equation to verify:
2(140) + 100 = 280 + 100 = 380ft.
So, the equation is satisfied and the dimensions of the playground that can be fenced in using the donated fencing are 140ft by 100ft.