Length and breadth of a rectangle are increased by 40% and 70% respectively. What will be the percentage increase in the area of rectangle?

Options

A. 118
B. 110
C. 138
D. 128

Answer

To find the percentage increase in the area of a rectangle when its length and breadth are increased by 40% and 70% respectively, we can follow these steps:

### Step 1: Define the original dimensions
Let the original length of the rectangle be \( L \) and the original breadth be \( B \).

### Step 2: Calculate the new dimensions
- The new length after a 40% increase is:
\[ \text{New Length} = L + 0.4L = 1.4L \]
- The new breadth after a 70% increase is:
\[ \text{New Breadth} = B + 0.7B = 1.7B \]

### Step 3: Calculate the original area
The original area \( A_{old} \) of the rectangle is given by:
\[ A_{old} = L \times B \]

### Step 4: Calculate the new area
The new area \( A_{new} \) of the rectangle after the increases is:
\[ A_{new} = \text{New Length} \times \text{New Breadth} = (1.4L) \times (1.7B) \]
Calculating this gives:
\[ A_{new} = 1.4L \times 1.7B = 2.38LB \]

### Step 5: Calculate the increase in area
The increase in area \( \Delta A \) is:
\[ \Delta A = A_{new} - A_{old} = 2.38LB - LB = (2.38 - 1)LB = 1.38LB \]

### Step 6: Calculate the percentage increase in area
The percentage increase in area is given by:
\[ \text{Percentage Increase} = \left( \frac{\Delta A}{A_{old}} \right) \times 100 = \left( \frac{1.38LB}{LB} \right) \times 100 = 138\% \]

### Conclusion
The percentage increase in the area of the rectangle is **138%**.

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