A rectangular grass area ub a park measures 50 yards by 100 yards. The city wishes to put a uniform sidewalk around the grass area which would increase the area by 459 yd ^2. What is the width of sidewalk
To find the width of the sidewalk, we can start by calculating the area of the grassy area.
The grass area is a rectangle with dimensions 50 yards by 100 yards. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the grassy area is:
Area of grassy area = length × width = 50 yards × 100 yards = 5000 yd^2
The city wishes to put a uniform sidewalk around the grassy area, which would increase the overall area by 459 yd^2. So, we can find the new total area by adding the increase in area to the grassy area:
New total area = Area of grassy area + Increase in area = 5000 yd^2 + 459 yd^2 = 5459 yd^2
Now, the total area includes the grassy area, the sidewalk, and the area between them. We need to subtract the grassy area from the total area to find the area of the sidewalk and the empty space between the grassy area and the sidewalk:
Area of sidewalk + Empty space = New total area - Area of grassy area
Area of sidewalk + Empty space = 5459 yd^2 - 5000 yd^2 = 459 yd^2
Since the sidewalk is uniform, the empty space on all four sides of the grassy area will be the same. To find the width of the sidewalk, we can divide the empty space by 2 (since there are two sides with the same width of sidewalk):
Width of sidewalk = (Area of sidewalk + Empty space) / 2 = 459 yd^2 / 2 = 229.5 yards
Therefore, the width of the sidewalk around the grassy area would be 229.5 yards.