A children's park is 350m long and 200 m wide. It is surrounded by a pathway of uniform wittd. Suppose the total area of the park and the pathway is 74,464 meter square. How wide is the pathway?
To find the width of the pathway, we need to subtract the area of the park from the total area of the park and pathway combined.
1. Calculate the area of the park:
Area of the park = length × width = 350 m × 200 m = 70,000 m².
2. Subtract the area of the park from the total area of the park and pathway combined to find the area of the pathway:
Area of the pathway = Total area - Area of the park = 74,464 m² - 70,000 m² = 4,464 m².
3. Since the pathway has a uniform width, we can find the width by dividing the area of the pathway by the length of the park:
Width of the pathway = Area of the pathway / Length of the park = 4,464 m² / 350 m = 12.755 m.
Therefore, the width of the pathway is approximately 12.755 meters.
To find the width of the pathway, we will need to subtract the area of the children's park from the total area of the park and the pathway.
Given:
Length of the children's park = 350 m
Width of the children's park = 200 m
Total area of the park and pathway = 74,464 m^2
First, let's find the area of the children's park:
Area of the children's park = Length × Width
= 350 m × 200 m
= 70,000 m^2
Now, subtract the area of the children's park from the total area of the park and pathway to find the area of the pathway:
Area of the pathway = Total area of the park and pathway - Area of the children's park
= 74,464 m^2 - 70,000 m^2
= 4,464 m^2
Since the pathway has a uniform width, we can consider it as a rectangle with length and width.
Let's assume the width of the pathway is 'x' meters.
The area of the pathway can be calculated as:
Area of the pathway = Length × Width
= (350 m + 2x) × (200 m + 2x)
= 4,464 m^2
Now, we have a quadratic equation that needs to be solved to find 'x'.
Expanding the equation:
(350 m + 2x) × (200 m + 2x) = 4,464 m^2
70,000 m^2 + 700x + 400x + 4x^2 = 4,464 m^2
4x^2 + 1,100x + 70,000 - 4,464 = 0
4x^2 + 1,100x - 65,536 = 0
Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 4, b = 1,100, and c = -65,536
Calculating the value of 'x' using the quadratic formula, we get:
x = (-1,100 ± √(1,100^2 - 4 × 4 × -65,536)) / (2 × 4)
x = (-1,100 ± √(1,210,000 + 1,049,152)) / 8
x = (-1,100 ± √2,259,152) / 8
x ≈ (-1,100 ± 1,502.77) / 8
Solving for x using both the positive and negative values:
x ≈ (-1,100 + 1,502.77) / 8
x ≈ 402.77 / 8
x ≈ 50.35
x ≈ (-1,100 - 1,502.77) / 8
x ≈ -2,602.77 / 8
x ≈ -325.35
Since the width cannot be negative, we can ignore the negative solution. Therefore, the width of the pathway is approximately 50.35 meters.
subtract the inner park from the total area:
(350+2w)(200+2w)-350*200 = 74464