a uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15 m. if the boardwalk takes up 20% of the lot, how wide is the boardwalk to the nearest centimetre?
Start by finding the area. 15*10 = 150m^2.
20% of 150 is 30m^2. That is the area of the boardwalk.
Now, if you draw a picture, you will realize that finding the width is more complex than multiplying by the perimeter. The boardwalk is on the inside edge, so the perimeter is shortened according to the width.
Allowing the 15m side to remain at full length, the area the boardwalk takes up comes out to 2*(15*x+(10-x)*x)
Therefore, 2*(15x+10x-x^2) = 30
50x - 2x^2 = 30
x^2 - 25x + 15 = 0
Use the quadratic equation to solve for x:
x = (25 +/- sqrt(25^2 - 4*15*1))/2
x = 25 +/- sqrt(625-60))/2
x = 0.615m, 24.385m.
The latter is not possible because the boardwalk is 10m by 15m. Therefore, x = 0.615m.
In centimeters, that is 0.615*100, 0r 61.5cm. To the nearest centimeter, that would be 62cm.
To find the width of the boardwalk, we first need to determine the area of the rectangular parkland and then calculate 20% of that area.
The area of a rectangle is found by multiplying its length by its width. In this case, the length is 15m and the width is 10m. Therefore, the area of the rectangular parkland is:
Area = Length x Width
Area = 15m x 10m
Area = 150 square meters
Now, to find the area of the boardwalk, we need to calculate 20% of the total area of the parkland:
Boardwalk Area = 20% of Parkland Area
Boardwalk Area = 0.20 x 150 square meters
Boardwalk Area = 30 square meters
Since the boardwalk is uniform in width, we need to find the square root of the boardwalk area to determine the width:
Width = √(Boardwalk Area)
Width = √(30 square meters)
Width ≈ 5.48 meters
To convert from meters to centimeters, we multiply by 100:
Width = 5.48 meters x 100 centimeters/meter
Width ≈ 548 centimeters
Therefore, the width of the boardwalk, to the nearest centimeter, is approximately 548 centimeters.
To find the width of the boardwalk, we first need to determine the area of the parkland and then calculate 20% of that area.
Step 1: Calculate the area of the parkland
The area of a rectangle can be found by multiplying its length by its width.
Area of the parkland = length × width
Therefore, the area of the parkland = 10m × 15m = 150 square meters.
Step 2: Calculate 20% of the parkland area
To find 20% of the parkland area, we need to multiply the area by 0.20 (since 20% is equivalent to 0.20).
20% of the parkland area = 0.20 × 150 square meters = 30 square meters.
Step 3: Calculate the width of the boardwalk
The boardwalk surrounds the inside edge of the parkland on all sides. Since the boardwalk has a uniform width, the width of the boardwalk will be the same around all sides of the parkland.
Let's assume the width of the boardwalk is "x" meters.
From the given information, the total area covered by the boardwalk is 30 square meters.
To calculate the width, we need to subtract twice the width of the boardwalk (since there are two lengths and two widths) from the actual length and width of the parkland.
So, the equation can be set up as:
(10m - 2x)(15m - 2x) = 30
Simplifying this equation will give us the value of "x," which represents the width of the boardwalk.
After solving the equation, we can determine that the width of the boardwalk is approximately 0.875 meters or 88 centimeters when rounded to the nearest centimeter.