To find the percentage change in width needed for the area of the rectangle to decrease by 2% after increasing the length by 40%, we can follow these steps:
1. Let's assume the original length of the rectangle is 100 units (for easy calculation).
2. After increasing the length by 40%, the new length becomes 100 + 40% of 100 = 100 + 40 = 140 units.
3. The area of a rectangle is given by the formula: Area = Length x Width.
4. Let the original width be x units. Therefore, the original area = 100 * x = 100x square units.
5. The new area after increasing the length by 40% would be 140 * x = 140x square units.
6. We are given that the new area is 2% less than the original area.
7. This means 140x = 0.98 * 100x (as the area decreased by 2%).
8. Solving the equation, we get: 140x = 98x. Dividing both sides by 98x gives 140 / 98 = 1.4286 ≈ 1.43.
9. This implies that the width needs to be decreased by approximately 43% for the area to decrease by 2%.
10. However, the provided answer choices do not include 43%. Among the given options, the closest percentage is a decrease by 40% (Option D).
Therefore, the most suitable answer among the given choices is:
D. Decreased by 40%
