Math Problem Statement

A farmer has a rectangular field of length 240 m and breadth 180 m respectively. He wants to fence it with 3 rounds of rope. What is the total length of rope he must use? Find the cost of fencing a rectangular park of length 250 m and breadth 175 m at the rate of ₹12 per meter. Find the distance traveled by Shaina if she takes three rounds of a square park of side 70 m.

Solution

The uploaded image contains handwritten mathematical problems and their solutions. Let me transcribe and verify the solutions for clarity and correctness.


Question 1:

A farmer has a rectangular field of length 240 m and breadth 180 m respectively. He wants to fence it with 3 rounds of rope. What is the total length of rope he must use?

Solution:

  1. Length of field = 240 m
  2. Breadth of field = 180 m

The perimeter of the rectangular field is calculated as:
Perimeter=2×(Length+Breadth)\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})
Perimeter=2×(240+180)=2×420=840m\text{Perimeter} = 2 \times (240 + 180) = 2 \times 420 = 840 \, \text{m}

For 3 rounds of rope:
Total length of rope=3×Perimeter=3×840=2520m\text{Total length of rope} = 3 \times \text{Perimeter} = 3 \times 840 = 2520 \, \text{m}


Question 2:

Find the cost of fencing a rectangular park of length 250 m and breadth 175 m at the rate of ₹12 per meter.

Solution:

  1. Length of park = 250 m
  2. Breadth of park = 175 m

The perimeter of the rectangular park is:
Perimeter=2×(Length+Breadth)\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})
Perimeter=2×(250+175)=2×425=850m\text{Perimeter} = 2 \times (250 + 175) = 2 \times 425 = 850 \, \text{m}

The cost of fencing is calculated as:
Cost=Perimeter×Rate per meter\text{Cost} = \text{Perimeter} \times \text{Rate per meter}
Cost=850×12=10,200\text{Cost} = 850 \times 12 = ₹10,200


Question 3:

Find the distance traveled by Shaina if she takes three rounds of a square park of side 70 m.

Solution:

  1. Side of the square park = 70 m

The perimeter of the square park is:
Perimeter=4×Side\text{Perimeter} = 4 \times \text{Side}
Perimeter=4×70=280m\text{Perimeter} = 4 \times 70 = 280 \, \text{m}

For 3 rounds, the total distance is:
Total distance=3×Perimeter=3×280=840m\text{Total distance} = 3 \times \text{Perimeter} = 3 \times 280 = 840 \, \text{m}


Summary of Solutions:

  1. Total length of rope: 2520 m
  2. Cost of fencing: ₹10,200
  3. Distance traveled by Shaina: 840 m

Let me know if you want detailed explanations for any step!


Related Questions:

  1. What is the formula for the perimeter of a rectangle?
  2. How does the cost change if the rate per meter increases to ₹15?
  3. What is the total length of the rope for 5 rounds around the rectangular field?
  4. How is the perimeter of a square related to its side length?
  5. If the side of the square park was increased to 100 m, how far would Shaina travel in 3 rounds?

Tip:

Always double-check your calculations, especially when multiplying or adding large numbers.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Perimeter
Rectangles
Squares
Cost Calculation

Formulas

Perimeter of rectangle = 2 × (Length + Breadth)
Perimeter of square = 4 × Side
Total cost = Perimeter × Rate

Theorems

-

Suitable Grade Level

Grades 6-8