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A rectangular plot has a length of 50 meters and a width of 30 meters. If a path

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Question: A rectangular plot has a length of 50 meters and a width of 30 meters. If a path of 2 meters width is built around it, what is the area of the path?

Options:

  1. 320 m²
  2. 400 m²
  3. 600 m²
  4. 800 m²

Correct Answer: 400 m²

Solution: 

Total area with path = (50 + 4) × (30 + 4) = 54 × 34 = 1836 m². Area of the plot = 50 × 30 = 1500 m². Area of the path = 1836 - 1500 = 336 m².

A rectangular plot has a length of 50 meters and a width of 30 meters. If a path

Practice Questions

Q1
A rectangular plot has a length of 50 meters and a width of 30 meters. If a path of 2 meters width is built around it, what is the area of the path?
  1. 320 m²
  2. 400 m²
  3. 600 m²
  4. 800 m²

Questions & Step-by-Step Solutions

A rectangular plot has a length of 50 meters and a width of 30 meters. If a path of 2 meters width is built around it, what is the area of the path?
  • Step 1: Identify the dimensions of the rectangular plot. The length is 50 meters and the width is 30 meters.
  • Step 2: Calculate the area of the rectangular plot using the formula: Area = Length × Width. So, Area = 50 × 30.
  • Step 3: Calculate the area of the rectangular plot: 50 × 30 = 1500 square meters.
  • Step 4: Determine the width of the path around the plot, which is 2 meters.
  • Step 5: Calculate the new dimensions of the plot including the path. The new length is 50 + 2 + 2 = 54 meters (adding 2 meters on each side).
  • Step 6: Calculate the new width including the path. The new width is 30 + 2 + 2 = 34 meters (adding 2 meters on each side).
  • Step 7: Calculate the total area including the path using the formula: Total Area = New Length × New Width. So, Total Area = 54 × 34.
  • Step 8: Calculate the total area: 54 × 34 = 1836 square meters.
  • Step 9: Find the area of the path by subtracting the area of the plot from the total area: Area of the path = Total Area - Area of the plot.
  • Step 10: Calculate the area of the path: 1836 - 1500 = 336 square meters.
  • Area Calculation – Understanding how to calculate the area of rectangles and the effect of adding dimensions.
  • Perimeter and Area Relationship – Recognizing how the addition of a path affects the overall dimensions and area.
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