How much percent will the area of a rectangle exceed if its length is increased by `23%` and breadth is increased by` 9%` .

Answer

To solve the problem of how much percent the area of a rectangle will exceed when its length is increased by 23% and its breadth is increased by 9%, we can follow these steps:

### Step 1: Define the original dimensions of the rectangle
Let the original length (L) of the rectangle be 100 units and the original breadth (B) be 100 units.

### Step 2: Calculate the original area of the rectangle
The area (A) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
So, the original area is:
\[ A = 100 \times 100 = 10000 \text{ square units} \]

### Step 3: Calculate the new dimensions after the increase
- The new length after a 23% increase:
\[ \text{New Length} = L + (23\% \text{ of } L) = 100 + (0.23 \times 100) = 100 + 23 = 123 \text{ units} \]

- The new breadth after a 9% increase:
\[ \text{New Breadth} = B + (9\% \text{ of } B) = 100 + (0.09 \times 100) = 100 + 9 = 109 \text{ units} \]

### Step 4: Calculate the new area of the rectangle
Now, we can calculate the new area (A') using the new dimensions:
\[ A' = \text{New Length} \times \text{New Breadth} \]
\[ A' = 123 \times 109 \]

Calculating this:
\[ A' = 123 \times 109 = 13407 \text{ square units} \]

### Step 5: Calculate the increase in area
To find the increase in area, we subtract the original area from the new area:
\[ \text{Increase in Area} = A' - A = 13407 - 10000 = 3407 \text{ square units} \]

### Step 6: Calculate the percentage increase in area
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{3407}{10000} \right) \times 100 = 34.07\% \]

### Final Answer
The area of the rectangle will exceed by **34.07%**.

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