6. If the length of a rectangle is increased by 30% and the width of the same rectangle is decreased by 30%, what is the effect on the area of the rectangle?
Answer: D
The area of the rectangle is decreased by 9%.
When the length of a rectangle is increased by 30% and the width is decreased by 30%, the overall effect on the area results in a decrease of 9%.
A) It is increased by 60%.
This option is incorrect because an increase of 30% in length does not lead to a 60% increase in area when coupled with a 30% decrease in width. The calculations show that the area actually decreases.
B) It is unchanged.
This option is also incorrect. A change in dimensions of the rectangle (increasing length and decreasing width) results in a net change in area. Therefore, the area cannot remain unchanged.
C) It is decreased by 15%.
This choice is incorrect because the calculations show that the area decreases by only 9%. A 15% decrease does not accurately reflect the combined effects of the dimensional changes.
D) It is decreased by 9%.
This option is correct. The increase in length by 30% and the decrease in width by 30% lead to a reduction in area, which can be calculated to determine that the net effect is a 9% decrease.
Conclusion
The correct answer, a 9% decrease in area, results from the interplay of the increased length and decreased width. Other options fail to accurately reflect the mathematical relationship between the changes in dimensions and their impact on the area, confirming that D is the only valid conclusion based on the given conditions.