If the length of a rectangle is increased by 40% what would be the percentage decrease (correct to one place of decimal) in the width to maintain the same area ?

Options

A. `37.5%`
B. `33.5%`
C. `28.6%`
D. `42.5%`

Answer

To solve the problem of finding the percentage decrease in the width of a rectangle when the length is increased by 40% while maintaining the same area, we can follow these steps:

### Step-by-step Solution:

1. **Define Initial Length and Width**:
Let the initial length of the rectangle be \( L \) and the initial width be \( W \).

2. **Calculate the New Length**:
If the length is increased by 40%, the new length \( L' \) can be calculated as:
\[ L' = L + 0.4L = 1.4L \]

3. **Calculate the Initial Area**:
The initial area \( A \) of the rectangle is given by:
\[ A = L \times W \]

4. **Set Up the Equation for the New Area**:
To maintain the same area after increasing the length, the area with the new dimensions must also equal \( A \):
\[ A = L' \times W' = 1.4L \times W' \]
Setting the areas equal gives:
\[ L \times W = 1.4L \times W' \]

5. **Solve for the New Width**:
Dividing both sides by \( L \) (assuming \( L \neq 0 \)):
\[ W = 1.4 \times W' \]
Rearranging gives:
\[ W' = \frac{W}{1.4} \]

6. **Calculate the Decrease in Width**:
The decrease in width \( D \) is:
\[ D = W - W' = W - \frac{W}{1.4} \]
Simplifying this:
\[ D = W \left(1 - \frac{1}{1.4}\right) = W \left(\frac{1.4 - 1}{1.4}\right) = W \left(\frac{0.4}{1.4}\right) = \frac{2W}{7} \]

7. **Calculate the Percentage Decrease**:
The percentage decrease in width is given by:
\[ \text{Percentage Decrease} = \left(\frac{D}{W}\right) \times 100 = \left(\frac{\frac{2W}{7}}{W}\right) \times 100 = \frac{2}{7} \times 100 \]
Calculating this gives:
\[ \frac{2}{7} \times 100 \approx 28.57\% \]
Rounding to one decimal place, we get:
\[ \text{Percentage Decrease} \approx 28.6\% \]

### Final Answer:
The percentage decrease in the width to maintain the same area is approximately **28.6%**.