Question:
The number of acid lime plants under Triangular system of planting per hectare when planted at a spacing of \(5m \times 5m\) will be
The number of acid lime plants under Triangular system of planting per hectare when planted at a spacing of \(5m \times 5m\) will be
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Remember planting system formulas:
- Square planting: Plants/ha = 10000 (S × S)
- Rectangular: Plants/ha = 10000 (L × B)
- Triangular: Plants/ha = 10000 (S^2) × 1.154
- Hexagonal: Plants/ha = 10000 (S^2) × 1.154 (same as triangular)
Triangular planting accommodates 15.4% more plants than square planting.
- Square planting: Plants/ha = 10000 (S × S)
- Rectangular: Plants/ha = 10000 (L × B)
- Triangular: Plants/ha = 10000 (S^2) × 1.154
- Hexagonal: Plants/ha = 10000 (S^2) × 1.154 (same as triangular)
Triangular planting accommodates 15.4% more plants than square planting.
Updated On: Aug 19, 2026
- 357
- 461
- 400
- 320
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
This question tests knowledge of planting systems and calculation of plant population.
Step 2: Key Formula or Approach:
For Triangular system of planting, the formula for calculating the number of plants per hectare is:
\[ \text{Number of plants per hectare} = \frac{10000}{\text{Area per plant}} \] In triangular planting, the area per plant is given by:
\[ \text{Area per plant} = \frac{(\text{Spacing})^2}{0.866} \] where 0.866 is the factor for equilateral triangle arrangement.
Step 3: Detailed Explanation:
Given spacing = \(5m \times 5m\)
First, calculate the area occupied by each plant in triangular system:
\[ \text{Area per plant} = \frac{5 \times 5}{0.866} = \frac{25}{0.866} = 28.87 \text{ sq m} \] Now, calculate the number of plants per hectare:
\[ \text{Number of plants} = \frac{10000}{28.87} = 346.3 \] Wait, this gives approximately 346 plants.
But the standard formula for triangular planting is:
\[ \text{Plants per hectare} = \frac{10000}{S^2} \times 1.154 \] where \(S\) is the spacing in meters.
\[ \text{Plants per hectare} = \frac{10000}{25} \times 1.154 = 400 \times 1.154 = 461.6 \] Thus, approximately 461 plants per hectare.
Option (B) 461 is the correct answer.
Step 4: Final Answer:
Thus, the number of acid lime plants under triangular system is 461, which corresponds to option (B).
[0.5cm]
This question tests knowledge of planting systems and calculation of plant population.
Step 2: Key Formula or Approach:
For Triangular system of planting, the formula for calculating the number of plants per hectare is:
\[ \text{Number of plants per hectare} = \frac{10000}{\text{Area per plant}} \] In triangular planting, the area per plant is given by:
\[ \text{Area per plant} = \frac{(\text{Spacing})^2}{0.866} \] where 0.866 is the factor for equilateral triangle arrangement.
Step 3: Detailed Explanation:
Given spacing = \(5m \times 5m\)
First, calculate the area occupied by each plant in triangular system:
\[ \text{Area per plant} = \frac{5 \times 5}{0.866} = \frac{25}{0.866} = 28.87 \text{ sq m} \] Now, calculate the number of plants per hectare:
\[ \text{Number of plants} = \frac{10000}{28.87} = 346.3 \] Wait, this gives approximately 346 plants.
But the standard formula for triangular planting is:
\[ \text{Plants per hectare} = \frac{10000}{S^2} \times 1.154 \] where \(S\) is the spacing in meters.
\[ \text{Plants per hectare} = \frac{10000}{25} \times 1.154 = 400 \times 1.154 = 461.6 \] Thus, approximately 461 plants per hectare.
Option (B) 461 is the correct answer.
Step 4: Final Answer:
Thus, the number of acid lime plants under triangular system is 461, which corresponds to option (B).
[0.5cm]
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