Math Problem Statement

A field is 62 meters long and 24 meters wide. How many meters of wire will be required to put up 2 wire fences around the farm? How many plants can be planted in the field if plants are to be planted at a distance of one meter each?

Solution

Part 1: Calculating Wire Required for Two Fences

The perimeter of the field is given by the formula: P=2×(length+width)P = 2 \times (\text{length} + \text{width}) Substituting the values: P=2×(62+24)=2×86=172metersP = 2 \times (62 + 24) = 2 \times 86 = 172 \, \text{meters}

Since two wire fences are to be set up, the total wire required is: Wire required=2×172=344meters\text{Wire required} = 2 \times 172 = 344 \, \text{meters}

Part 2: Calculating Number of Plants

The area of the field is: Area=length×width\text{Area} = \text{length} \times \text{width} Substituting the values: Area=62×24=1488square meters\text{Area} = 62 \times 24 = 1488 \, \text{square meters}

If plants are to be planted at a distance of 1 meter apart, the number of plants equals the total area: Number of plants=1488\text{Number of plants} = 1488

Final Results:

  1. Wire required for two fences: 344 meters
  2. Number of plants that can be planted: 1488

Would you like me to explain any of the steps further or assist with related problems?


Related Questions:

  1. What would happen if the dimensions of the field changed?
  2. How would the calculation differ if three wire fences were needed?
  3. How to calculate wire cost if the price per meter is given?
  4. How many plants fit if spacing between plants is increased to 2 meters?
  5. How to calculate the cost of planting if each plant costs a specific amount?

Tip:

To estimate the perimeter of any rectangular shape, remember to double the sum of its length and width. This formula is simple yet powerful for many real-life problems!

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Math Problem Analysis

Mathematical Concepts

Perimeter
Area
Multiplication
Measurement

Formulas

Perimeter of a rectangle: P = 2 × (length + width)
Area of a rectangle: A = length × width

Theorems

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Suitable Grade Level

Grades 6-8