The length of a rectangle is ten time while breadth become half is the percentage change in area ?

Options

A. 50
B. 75
C. 500
D. 100

Answer

To solve the problem of finding the percentage change in the area of a rectangle when the length is increased to ten times and the breadth is halved, we can follow these steps:

### Step-by-step Solution:

1. **Define the Original Dimensions**:
- Let the original length of the rectangle be \( L \).
- Let the original breadth of the rectangle be \( B \).

2. **Calculate the Original Area**:
- The area \( A_1 \) of the rectangle is given by the formula:
\[ A_1 = \text{Length} \times \text{Breadth} = L \times B \]

3. **Define the New Dimensions**:
- The new length of the rectangle is \( 10L \) (ten times the original length).
- The new breadth of the rectangle is \( \frac{B}{2} \) (half of the original breadth).

4. **Calculate the New Area**:
- The area \( A_2 \) of the rectangle with the new dimensions is:
\[ A_2 = \text{New Length} \times \text{New Breadth} = 10L \times \frac{B}{2} \]
- Simplifying this gives:
\[ A_2 = 10L \times \frac{B}{2} = 5LB \]

5. **Calculate the Change in Area**:
- The change in area \( \Delta A \) can be calculated as:
\[ \Delta A = A_2 - A_1 = 5LB - LB = 4LB \]

6. **Calculate the Percentage Change in Area**:
- The percentage change in area is given by the formula:
\[ \text{Percentage Change} = \left( \frac{\Delta A}{A_1} \right) \times 100 \]
- Substituting the values we have:
\[ \text{Percentage Change} = \left( \frac{4LB}{LB} \right) \times 100 = 4 \times 100 = 400\% \]

### Final Answer:
The percentage change in area is **400%**.