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(b) The length and width of a rectangular plot of land are 150 m and 120 m, respectively. A footpath of regular width is added to the boundary of the plot, and the total area of the plot becomes 2800 m² more than its original area. Find the width of the footpath.

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.

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