The length of a rectangle is increased by 60%. By what percent should the width be decreased to maintain the same area?

Answer

To solve the problem step by step, we can follow these instructions:

### Step-by-Step Solution:

1. **Define the Original Dimensions**:
Let the original length of the rectangle be \( L = 100 \) meters and the original width be \( W = 100 \) meters.

2. **Calculate the Original Area**:
The area \( A \) of a rectangle is given by the formula:
\[ A = L \times W \]
Substituting the values:
\[ A = 100 \times 100 = 10,000 \text{ square meters} \]

3. **Increase the Length**:
The length is increased by 60%. Therefore, the new length \( L' \) can be calculated as:
\[ L' = L + 0.6L = 100 + 60 = 160 \text{ meters} \]

4. **Let the New Width be \( X \)**:
We need to find the new width \( X \) such that the new area remains equal to the original area. The new area \( A' \) can be expressed as:
\[ A' = L' \times X = 160 \times X \]

5. **Set the New Area Equal to the Original Area**:
To maintain the same area, we set the new area equal to the original area:
\[ 160 \times X = 10,000 \]

6. **Solve for \( X \)**:
Rearranging the equation gives:
\[ X = \frac{10,000}{160} = 62.5 \text{ meters} \]

7. **Calculate the Decrease in Width**:
The original width was 100 meters, and the new width is 62.5 meters. The decrease in width is:
\[ \text{Decrease} = 100 - 62.5 = 37.5 \text{ meters} \]

8. **Calculate the Percentage Decrease**:
The percentage decrease in width can be calculated using the formula:
\[ \text{Percentage Decrease} = \left(\frac{\text{Decrease}}{\text{Original Width}} \times 100\right) \]
Substituting the values:
\[ \text{Percentage Decrease} = \left(\frac{37.5}{100} \times 100\right) = 37.5\% \]

### Final Answer:
The width should be decreased by **37.5%** to maintain the same area.