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?

Rationale

It 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 approximately 9%. This is calculated by considering the new dimensions and their impact on the area formula.

A (It is increased by 60%.) YOUR ANSWER

This choice suggests that the area increases significantly due to the changes in dimensions. However, while the length increases by 30%, the width's decrease by 30% counteracts this effect. The area does not simply add these percentages together; instead, the area calculation shows a net decrease.

B (It is unchanged.) YOUR ANSWER

This choice implies that the area remains the same despite the changes in length and width. However, since the length and width are altered by different percentages, the area will definitely change. Specifically, the increase in length does not compensate for the decrease in width, leading to a change in total area.

C (It is decreased by 15%.) YOUR ANSWER

This option suggests a larger decrease in area than what actually occurs. The calculations reveal that the combined effect of a 30% increase in length and a 30% decrease in width results in a smaller net decrease of approximately 9%, not 15%.

D (It is decreased by 9%.) CORRECT

This choice accurately reflects the result of the area change. The new area can be calculated based on the modified dimensions, leading to a net decrease of about 9%. This calculation takes into account the opposing effects of the length increase and width decrease.

Conclusion

The adjustments to the rectangle's dimensions—an increase in length and a decrease in width—result in a complex interaction impacting the area. Specifically, while one dimension increases, the other decreases enough to cause an overall decrease of 9% in area. Understanding these percentages and their respective effects is crucial for accurately determining changes in geometric properties.

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?

It is decreased by 9%.

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