Math Problem Statement
A rectangular grassy lawn measuring 40m by 25m is to be surrounded externally by a path which is 2m wide. Calculate the cost of levelling the path at the rate of ` 8.25 per square metre.
Solution
We are given that a rectangular grassy lawn has dimensions 40 meters by 25 meters, and it is to be surrounded by a 2-meter-wide path. The task is to find the cost of levelling the path, which is calculated at a rate of 8.25 per square meter.
Step 1: Calculate the area of the lawn.
The area of the rectangular lawn is:
Step 2: Calculate the total area of the lawn and the path.
The path is 2 meters wide and surrounds the lawn externally. Therefore, the overall dimensions (including the path) will be:
Now, calculate the total area (lawn + path):
Step 3: Calculate the area of the path.
The area of the path is the difference between the total area and the area of the lawn:
Step 4: Calculate the cost of levelling the path.
The cost of levelling the path is calculated by multiplying the area of the path by the cost per square meter:
Thus, the cost of levelling the path is 2271 currency units.
Would you like further clarification or details on any of the steps? Here are a few related questions:
- What would be the area of the path if the width was changed to 3 meters?
- How would the cost change if the rate per square meter was increased to 10 currency units?
- How do you calculate the area of a rectangle when given its length and width?
- How would you approach this problem if the path had varying widths along the lawn?
- How can you calculate the cost of levelling for different shapes like circular lawns or irregular plots?
Tip: When dealing with problems involving paths around a rectangular area, always calculate the total area (including the path) and subtract the area of the original object (lawn) to get the area of the path.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Cost Calculation
Formulas
Area of a rectangle = Length × Width
Total Area (including path) = (Length + 2 × Path Width) × (Width + 2 × Path Width)
Area of Path = Total Area - Lawn Area
Cost = Area of Path × Rate per Square Meter
Theorems
Basic Area Theorem for Rectangles
Suitable Grade Level
Grades 6-8
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