Final answer:
To find the length of the unfenced side of a rectangular playground, one must know the total amount of available fencing and the length of one of the fenced sides. From there, the formula for the perimeter can be used to calculate the missing dimension.
Step-by-step explanation:
The student's question pertains to finding the length of the unfenced side of a rectangular playground where the fourth side is along the school building and therefore doesn't require fencing. To solve this, it's assumed that the total amount of fencing available is known but not provided in the question's text. The formula for the perimeter P of a rectangle is P = 2l + 2w, where l is the length and w is the width. Since one side is along the school building, the total fencing needed equals the sum of the other three sides: Fencing = 2w + l. If the length of one of the fenced sides (width or length) is known, you can rearrange this formula to solve for the missing dimension. For example, if you know the total fencing (which is essentially the perimeter minus the unfenced side) and the length of one side, you can calculate the width, and vice versa.
An example to illustrate this might be if the school has 70 meters of fencing, and one of the lengths is known to be 20 meters. The fencing needed for the two widths would be 70 - 20 = 50 meters. Since there are two widths, each width would be 50 / 2 = 25 meters. Therefore, the unfenced side, which is the length, would also be 20 meters in this scenario.