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?

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:

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: