Math Problem Statement

Solve it

A garden 100 m long and 50 m wide has a road 3 m wide all around the garden. Find the cost of paving the road at the rate of Rs. 250 per m².

Solution

Let's break down the problem:

Given:

  • The garden is 100 m long and 50 m wide.
  • There is a road of 3 m wide around the garden.
  • The cost of paving the road is Rs. 250 per square meter.

To Find:

The total cost of paving the road.

Approach:

  1. Area of the garden (without the road):

    • Length = 100 m
    • Width = 50 m Area of garden=Length×Width=100×50=5000m2\text{Area of garden} = \text{Length} \times \text{Width} = 100 \times 50 = 5000 \, \text{m}^2
  2. Area of the garden including the road:

    • Since the road is around the garden, the total dimensions increase by 3 m on each side.
    • New Length = 100+2×3=106m100 + 2 \times 3 = 106 \, \text{m}
    • New Width = 50+2×3=56m50 + 2 \times 3 = 56 \, \text{m} Area of garden with road=New Length×New Width=106×56=5936m2\text{Area of garden with road} = \text{New Length} \times \text{New Width} = 106 \times 56 = 5936 \, \text{m}^2
  3. Area of the road: The area of the road is the difference between the area of the garden with the road and the area of the garden without the road: Area of road=Area with roadArea of garden=59365000=936m2\text{Area of road} = \text{Area with road} - \text{Area of garden} = 5936 - 5000 = 936 \, \text{m}^2

  4. Cost of paving the road: The cost is given as Rs. 250 per square meter. Cost=936×250=234000Rs\text{Cost} = 936 \times 250 = 234000 \, \text{Rs}

Answer:

The cost of paving the road is Rs. 234,000.

Would you like more details, or do you have any further questions?

Here are 5 related questions for practice:

  1. If the cost per square meter increased to Rs. 300, what would be the new total cost?
  2. How much area would the road cover if the garden was square, with a side length of 60 meters?
  3. What would be the cost if the road was only 2 meters wide instead of 3 meters?
  4. How would the area of the road change if the garden was 150 m long and 70 m wide?
  5. How much would it cost to pave a circular road with a radius of 5 meters around a circular garden?

Tip: When calculating areas, always account for the increase in dimensions on both sides when something surrounds a given area.

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Math Problem Analysis

Mathematical Concepts

Area Calculation
Cost Calculation
Geometry

Formulas

Area = Length × Width
Area of the garden with road = (Length + 2 × Road Width) × (Width + 2 × Road Width)
Cost = Area of road × Cost per square meter

Theorems

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Suitable Grade Level

Grades 6-8