Problem 6 · Test with easy numbers · 4 points
Made by AI and not reviewed by a real person.
The length of a rectangle is increased by 10% and its width is decreased by 10%. What happens to its area?
- it shrinks by 1%
- it stays the same
- it shrinks by 10%
- it grows by 1%
- it grows by 10%
Show a hint
- Start with a rectangle of unknown length and width. Describe how each percentage change affects a side, then consider how the changes combine when you multiply to find area.
- Let the original sides be L and W. Write the changed sides as 1.1L and 0.9W, then compare their product with the original area, LW.
Show the answer and solution
Answer: A — it shrinks by 1%
Let the original length be L and the width be W, so the original area is LW. The new area is (1.1L)(0.9W) = 0.99LW, or 99% of the original area. Therefore, it shrinks by 1%. The tempting answer “it stays the same” is wrong: a 10% increase in one side and a 10% decrease in the other do not cancel when the side lengths are multiplied.