Discussion
The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
Answer: B
Both dimensions grow, so multiply the two factors.
\[ \frac{A'}{A} = (1 + 0.10)(1 + 0.25) = 1.10 \times 1.25 = 1.375 \]
\[ \text{increase} = 1.375 - 1 = 0.375 = 37.5\% \]
Adding the percentages gives 35%; the extra 2.5% is the cross term \( 0.10 \times 0.25 \), the part of the rectangle that gains in both directions at once.
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