Measurement error on rectangle area: A student measures the length 20% less and the breadth 10% more than actual. If the true area is 200 sq cm, what area results from this mistaken measurement?
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A176 sq cm
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B206 sq cm
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C226 sq cm
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D316 sq cm
Answer
Correct Answer: 176 sq cm
Explanation
Introduction / Context:Area of a rectangle equals length * breadth. When each dimension is scaled by a factor, area scales by the product of those factors. This question focuses on compounded percentage changes in orthogonal dimensions.Given Data / Assumptions:
- True area A = L * B = 200 sq cm.
- Measured length = 80% of L (20% less) ⇒ 0.8L.
- Measured breadth = 110% of B (10% more) ⇒ 1.1B.
Concept / Approach:New measured area = (0.8L) * (1.1B) = 0.8 * 1.1 * (L * B) = 0.88 * A. Multiply the true area by 0.88 to get the resulting area; no need to know L and B separately.
Step-by-Step Solution:
Scale factors: length 0.8, breadth 1.1.Combined area factor = 0.8 * 1.1 = 0.88.Measured area = 0.88 * 200 = 176 sq cm.Verification / Alternative check:Consider L = 20, B = 10 ⇒ true area 200. Measured: 0.8*20 = 16 and 1.1*10 = 11 ⇒ area = 176, confirming.
Why Other Options Are Wrong:
- 206, 226, 316: Do not equal 0.88 * 200. They reflect incorrect handling of percentage compounding.
Common Pitfalls:Adding/subtracting percentages from the area directly (e.g., 20% − 10% = 10%) which ignores compounding across dimensions. Always multiply the dimension factors for area.
Final Answer:
176 sq cm