The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by

### Concept & Net Percentage Change When two dimensions of a 2D shape are increased by certain percentages, the net percentage change in area can be found using the effective percentage formula: $$ \text{Net Change} = x + y + \frac{xy}{100} $$ ### Step-by-Step Solution 1. Let the original side of the square be $10$ units. 2. The original area is $10 \times 10 = 100$ sq units. 3. The length is increased by $40\%$, so the new length is $10 + 4 = 14$ units. 4. The breadth is increased by $30\%$, so the new breadth is $10 + 3 = 13$ units. 5. The area of the resulting rectangle is $14 \times 13 = 182$ sq units. 6. The increase in area is $182 - 100 = 82$ sq units. 7. Since the original area is $100$, the percentage increase is exactly $82\%$. ### Exam Strategy & Shortcut Apply the net percentage change formula directly: Here, $x = +40$ and $y = +30$. $\text{Net \% Change} = 40 + 30 + \frac{40 \times 30}{100}$ $= 70 + \frac{1200}{100}$ $= 70 + 12 = 82\%$ ### Common Pitfall Simply adding the two percentage increases ($40\% + 30\% = 70\%$) without accounting for the compounded effect of both dimensions increasing simultaneously. ### Final Answer Therefore, the correct answer is **82%**.