16. A rectangle has length $$ L $$ and width $$ W $$ $$ L $$ is increased by $$ 20 \% $$ $$ W $$ is decreased by $$ 35 \% $$ Calculate the percentage reduction in the area of the rectangle.

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UpStudy AI · Accepted Answer

To determine the percentage reduction in the area of the rectangle, let's follow these steps:

1. **Original Area:**
   $$
   \text{Area}_{\text{original}} = L \times W
   $$

2. **New Dimensions:**
   - **Length ($$ L $$) is increased by $$ 20\% $$:**
     $$
     L_{\text{new}} = L + 0.20L = 1.20L
     $$
   - **Width ($$ W $$) is decreased by $$ 35\% $$:**
     $$
     W_{\text{new}} = W - 0.35W = 0.65W
     $$

3. **New Area:**
   $$
   \text{Area}_{\text{new}} = L_{\text{new}} \times W_{\text{new}} = 1.20L \times 0.65W = 0.78L \times W
   $$

4. **Change in Area:**
   $$
   \Delta \text{Area} = \text{Area}_{\text{original}} - \text{Area}_{\text{new}} = LW - 0.78LW = 0.22LW
   $$

5. **Percentage Reduction:**
   $$
   \text{Percentage Reduction} = \left( \frac{\Delta \text{Area}}{\text{Area}_{\text{original}}} \right) \times 100 = \left( \frac{0.22LW}{LW} \right) \times 100 = 22\%
   $$

**Conclusion:**
The area of the rectangle is reduced by **22%**.
The area of the rectangle is reduced by 22%.

A rectangle has length and width
is increased by
is decreased by
Calculate the percentage reduction in the area of the rectangle.

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A rectangle has length and width is increased by is decreased by Calculate the percentage reduction in the area of the rectangle.