25. If the length of a rectangle is increased by \( 40 \% \) and its width is decreased by \( 40 \% \), what is the effect on the rectangle's area? (A) The area is the same. (B) It increases by \( 16 \% \). (C) It increases by \( 20 \% \). (D) It decreases by \( 16 \% \). (E) It decreases by \( 20 \% \).

The area of a rectangle is calculated by multiplying its length and width. If the length is increased by \( 40\% \), it becomes \( 1.4L \) (where \( L \) is the original length). If the width is decreased by \( 40\% \), it becomes \( 0.6W \) (where \( W \) is the original width). The new area will be \( 1.4L \times 0.6W = 0.84LW \), which is \( 84\% \) of the original area. Therefore, the area decreases by \( 16\% \), making the correct answer (D) it decreases by \( 16\% \). Ever wondered how percentage changes can flip the outcomes of your calculations? With rectangles, a \( 40\% \) increase in length seems amazing, but pairing it with a \( 40\% \) decrease in width helps put things into perspective. It’s a delightful math rollercoaster, where expectations can get dashed if you're not careful! When it comes to geometry and area calculations, a common mistake might be to assume that equal percentage changes in two dimensions will balance each other out. This is a classic fallacy! Instead, remember that the area is a product of both dimensions. Utilize visuals, like drawing rectangles or using interactive tools, to help visualize the impact of these changes!