Triangular field cost → area → dimensions: The base is three times the altitude. If cultivation costs Rs 24.68 per hectare total Rs 333.18, find base and height (in metres).
Aptitude
Area
Difficulty: Medium
Choose an option
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AB=900;H=300
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BB=300;H=900
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CB=600;H=700
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DB=500;H=900
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ENone of these
Answer
Correct Answer: B=900;H=300
Explanation
Introduction / Context:Convert cost to area using the per-hectare rate, then use the relation between base and height to compute actual dimensions.
Given Data / Assumptions:
- Cost rate = Rs 24.68 per hectare.
- Total cost = Rs 333.18.
- Base b = 3h (h = altitude).
Concept / Approach:Area (hectares) = total cost / rate. Convert hectares to m^2 (1 ha = 10,000 m^2). For a triangle, Area = (1/2)*b*h = (1/2)*3h*h = 1.5*h^2.
Step-by-Step Solution:
Area = 333.18 / 24.68 = 13.5 hectares.Area in m^2 = 13.5 * 10000 = 135000.1.5*h^2 = 135000 ⇒ h^2 = 90000 ⇒ h = 300 m.b = 3h = 900 m.Verification / Alternative check:Area = 0.5*900*300 = 135000 m^2 = 13.5 ha; cost = 13.5*24.68 = 333.18 Rs.
Why Other Options Are Wrong:Only B=900;H=300 satisfies both the proportionality and the cost-derived area.
Common Pitfalls:Forgetting to convert hectares to square metres; mixing up base and height roles.
Final Answer:B=900;H=300