A uniform width boardwalk is built around the inside edge of a rectangular parkland that is 30 m by 5 m. If the boardwalk takes up 20% of the lot, how wide is the boardwalk to the nearest cm?
If the walk has width w, then since the parkland occupies 80% of the area,
(30-2w)(5-2w) = 0.80*30*5
w = 0.4396m
To find the width of the boardwalk, we first need to calculate the total area of the parkland.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 30 m and the width is 5 m. Therefore, the total area of the parkland is:
30 m * 5 m = 150 m²
Next, we need to calculate the area of the boardwalk, which is 20% of the total area of the parkland. To find this, we multiply the total area by 20% (or 0.20):
150 m² * 0.20 = 30 m²
Since the boardwalk has a uniform width, we can divide the total area of the boardwalk by its width to find the length of the boardwalk:
30 m² / width = length
Since we are looking for the width, we can rearrange the equation:
width = 30 m² / length
Now, we can substitute the values we know. The length of the boardwalk is the sum of the length and the width of the parkland:
length = 30 m + 5 m = 35 m
Therefore, the width of the boardwalk is:
width = 30 m² / 35 m = 0.857 m
Converting this to centimeters:
0.857 m * 100 cm/m = 85.7 cm
So, the width of the boardwalk to the nearest centimeter is approximately 86 cm.
To find the width of the boardwalk, we need to calculate 20% of the total area of the parkland.
First, let's calculate the total area of the parkland:
Area = Length x Width
Area = 30 m x 5 m
Area = 150 square meters
Now, we need to find 20% of the total area:
20% of 150 square meters = 0.2 x 150 square meters
20% of 150 square meters = 30 square meters
Since the boardwalk has a uniform width, the total area occupied by the boardwalk is equal to the width of the boardwalk multiplied by the perimeter of the parkland.
The perimeter of the parkland is calculated as follows:
Perimeter = 2 x (Length + Width)
Perimeter = 2 x (30 m + 5 m)
Perimeter = 2 x 35 m
Perimeter = 70 m
Let's assume the width of the boardwalk is w meters. Therefore, the area occupied by the boardwalk is given by:
Area of the boardwalk = Perimeter x w
Area of the boardwalk = 70 m x w
As given in the problem, the area occupied by the boardwalk is 30 square meters. So, we can equate the two values:
30 square meters = 70 m x w
Now, let's solve for the width of the boardwalk (w):
w = 30 square meters / 70 m
w = 0.4286 meters (rounded to four decimal places)
To convert the width to centimeters, multiply by 100:
w = 0.4286 meters x 100 cm/m
w = 42.86 cm (rounded to the nearest cm)
Therefore, the width of the boardwalk is approximately 42.86 centimeters.