Answer :
Final answer:
The width of the foot path is approximately 4.47m.
Explanation:
To find the width of the foot path, we need to consider the change in area of the plot after the foot path is added. Let's denote the width of the foot path as 'x'.
The original area of the plot is given by:
Original Area = length * width = 150m * 120m = 18000m²
After the foot path is added, the total area of the plot becomes 2800m² more than its original area:
New Area = Original Area + 2800m²
Substituting the values, we have:
New Area = 18000m² + 2800m² = 20800m²
The new length and width of the plot, including the foot path, can be expressed as:
New Length = length + 2x
New Width = width + 2x
Since the length and width of the plot remain the same, we can set up the following equation:
New Length * New Width = Original Area + 2800m²
Substituting the values, we have:
(length + 2x) * (width + 2x) = 18000m² + 2800m²
Expanding the equation, we get:
150m * 120m + 2x * 150m + 2x * 120m + 4x² = 20800m²
Simplifying the equation, we have:
18000m² + 2x * 150m + 2x * 120m + 4x² = 20800m²
Combining like terms, we get:
2x * 150m + 2x * 120m + 4x² = 2800m²
Further simplifying, we have:
300x + 240x + 4x² = 2800
Combining like terms, we get:
540x + 4x² = 2800
Setting the equation equal to zero, we have:
4x² + 540x - 2800 = 0
Now, we can solve this quadratic equation to find the value of 'x', which represents the width of the foot path.
Learn more about finding the width of a foot path added to a rectangular plot of land here:
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Final answer:
The width of the foot path is approximately 5.83 meters.
Explanation:
To find the width of the foot path, we can start by calculating the original area of the rectangular plot of land. The length of the plot is given as 150m and the width is given as 120m. We can use the formula for the area of a rectangle, which is length multiplied by width.
Original Area = Length × Width
Original Area = 150m × 120m
Original Area = 18000m²
Next, we need to calculate the new area of the plot after the foot path is added. Let's assume the width of the foot path is 'x' meters. Since the foot path is added to the boundary of the plot, the new length and new width will be increased by twice the width of the foot path.
New Length = Length + 2x
New Width = Width + 2x
New Area = New Length × New Width
New Area = (Length + 2x) × (Width + 2x)
New Area = (150m + 2x) × (120m + 2x)
Now, we can set up an equation using the given information that the new area is 2800m² more than the original area.
New Area - Original Area = 2800m²
(150m + 2x) × (120m + 2x) - 18000m² = 2800m²
Expanding the equation, we get:
18000m² + 420m²x + 300m²x + 4x² - 18000m² = 2800m²
420m²x + 300m²x + 4x² = 2800m²
720m²x + 4x² = 2800m²
4x² + 720m²x - 2800m² = 0
Now, we can solve this quadratic equation to find the value of 'x', which represents the width of the foot path.
Once we find the value of 'x', we can substitute it back into the equation for the new length and new width to get the final values.
To learn more about width here:
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