Math Problem Statement

Q4: A farmer has a rectangular field of length 240 m and breadth 180 m. He wants to fence it with 3 rounds of rope. What is the total length of rope he must buy? Q5: Find the cost of fencing a rectangular park of length 250 m and breadth 175 m at the rate of ₹12 per meter. Q6: Find the distance traveled by Shaim if she takes three rounds of a square park of side 70 m.

Solution

The image contains three mathematical problems related to perimeters and distances. Here's a detailed explanation for each:


Q4:

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

Solution:

  1. Length of field: 240m240 \, \text{m}
  2. Breadth of field: 180m180 \, \text{m}
  3. Perimeter of field: 2×(Length+Breadth)=2×(240+180)=2×420=840m2 \times (\text{Length} + \text{Breadth}) = 2 \times (240 + 180) = 2 \times 420 = 840 \, \text{m}
  4. For 3 rounds: 3×840=2520m3 \times 840 = 2520 \, \text{m}

Answer: 2520m2520 \, \text{m}


Q5:

Problem: 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: 250m250 \, \text{m}
  2. Breadth of park: 175m175 \, \text{m}
  3. Perimeter of park: 2×(Length+Breadth)=2×(250+175)=2×425=850m2 \times (\text{Length} + \text{Breadth}) = 2 \times (250 + 175) = 2 \times 425 = 850 \, \text{m}
  4. Cost of fencing: Perimeter×Rate per meter=850×12=10200\text{Perimeter} \times \text{Rate per meter} = 850 \times 12 = ₹10200

Answer: ₹10200


Q6:

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

Solution:

  1. Side of square park: 70m70 \, \text{m}
  2. Perimeter of square park: 4×Side=4×70=280m4 \times \text{Side} = 4 \times 70 = 280 \, \text{m}
  3. Distance for 3 rounds: 3×280=840m3 \times 280 = 840 \, \text{m}

Answer: 840m840 \, \text{m}


Would you like further clarifications on these problems? Here are some related questions:

  1. How is the perimeter formula for a rectangle derived?
  2. Why is the total rope required multiplied by 3 in Q4?
  3. What is the difference between area and perimeter?
  4. How would the cost change in Q5 if the rate per meter increased to ₹15?
  5. What would the total distance be in Q6 if Shaim took 5 rounds?

Tip: Always verify units and double-check calculations for accuracy.

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Math Problem Analysis

Mathematical Concepts

Perimeter of a rectangle
Cost calculation based on perimeter
Perimeter of a square
Distance calculation for multiple rounds

Formulas

Perimeter of a rectangle = 2 × (Length + Breadth)
Cost = Perimeter × Rate per meter
Perimeter of a square = 4 × Side
Total distance = Number of rounds × Perimeter

Theorems

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Suitable Grade Level

Grades 6-8