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 $$ 20 \% $$.

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To determine the effect on the rectangle's area when the length is increased by $$ 40\% $$ and the width is decreased by $$ 40\% $$, let's perform the following calculations:

1. **Initial Dimensions and Area:**
   - Let the original length be $$ L $$.
   - Let the original width be $$ W $$.
   - **Initial Area ($$ A_{\text{initial}} $$)**:
     $$
     A_{\text{initial}} = L \times W
     $$

2. **After Changes:**
   - **New Length**: 
     $$
     L_{\text{new}} = L + 0.40L = 1.40L
     $$
   - **New Width**: 
     $$
     W_{\text{new}} = W - 0.40W = 0.60W
     $$
   - **New Area ($$ A_{\text{new}} $$)**:
     $$
     A_{\text{new}} = L_{\text{new}} \times W_{\text{new}} = 1.40L \times 0.60W = 0.84LW
     $$

3. **Change in Area:**
   - Compare the new area to the original area:
     $$
     \frac{A_{\text{new}}}{A_{\text{initial}}} = \frac{0.84LW}{LW} = 0.84
     $$
   - This means the new area is $$ 84\% $$ of the original area.
   - **Percentage Change**:
     $$
     100\% - 84\% = 16\% \text{ decrease}
     $$

**Conclusion:** The rectangle's area decreases by $$ 16\% $$.

**Answer:** (D) It decreases by $$ 16 \% $$.
The rectangle's area decreases by 16%.

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