Find the percentage increase in the area of a rectangle if each of its sides (length and breadth) is increased by 20%.

Introduction:
This question tests scaling of area when both dimensions of a rectangle increase by the same percentage. Area is a two-dimensional quantity, so when both length and breadth are multiplied by a scale factor, the area is multiplied by the square of that factor. A common mistake is to add the percentages (20% + 20% = 40%), but that ignores the multiplicative effect. The correct method is to convert the percentage increase into a multiplication factor and multiply the factors for both sides.

Given Data / Assumptions:

• Length increases by 20%• Breadth increases by 20%• Original length = L, original breadth = B

Concept / Approach:
If a dimension increases by 20%, the multiplication factor is 1.20. New area = (1.20L) * (1.20B) = (1.20*1.20) * (L*B) = 1.44 * original area. The percentage increase is (1.44 - 1)*100 = 44%.

Step-by-Step Solution:
Step 1: Write original area.Original area = L * BStep 2: Increase each side by 20%.New length = 1.20LNew breadth = 1.20BStep 3: Compute new area.New area = (1.20L)*(1.20B) = 1.44 * L * BStep 4: Convert factor to percentage increase.Increase = (1.44 - 1)*100 = 0.44*100 = 44%

Verification / Alternative check:
Take L=10 and B=5. Original area = 50. New L=12, new B=6. New area=72. Increase=22. Percentage increase=22/50*100=44%. This numerical check confirms the formula result exactly.

Why Other Options Are Wrong:
40% is the common incorrect answer from adding 20% + 20%.22% and 33% come from partial scaling (only one dimension) or incorrect averaging.55% would require a larger scale factor than 1.20 on both sides.

Common Pitfalls:
• Adding percentages instead of multiplying scale factors.• Increasing only one side and thinking it applies to the whole area.• Rounding incorrectly and missing the exact 1.44 factor.

Final Answer:
The area increases by 44%.