If the length of a reactangle is increased by 20 % and breadth is decreased by 10 % find the net % change in the area of that reactangle .

Answer

To find the net percentage change in the area of a rectangle when the length is increased by 20% and the breadth is decreased by 10%, we can follow these steps:

### Step 1: Understand the Changes
- The length of the rectangle is increased by 20%.
- The breadth of the rectangle is decreased by 10%.

### Step 2: Define the Variables
Let:
- Original Length = L
- Original Breadth = B

### Step 3: Calculate the New Dimensions
- New Length = L + 20% of L = L + (20/100) * L = L * (1 + 0.20) = 1.20L
- New Breadth = B - 10% of B = B - (10/100) * B = B * (1 - 0.10) = 0.90B

### Step 4: Calculate the Original Area
- Original Area = Length × Breadth = L × B

### Step 5: Calculate the New Area
- New Area = New Length × New Breadth = (1.20L) × (0.90B)
- New Area = 1.20 × 0.90 × L × B = 1.08 × (L × B)

### Step 6: Calculate the Change in Area
- Change in Area = New Area - Original Area = (1.08 × (L × B)) - (L × B) = (1.08 - 1) × (L × B) = 0.08 × (L × B)

### Step 7: Calculate the Percentage Change in Area
- Percentage Change = (Change in Area / Original Area) × 100
- Percentage Change = (0.08 × (L × B) / (L × B)) × 100 = 0.08 × 100 = 8%

### Conclusion
The net percentage change in the area of the rectangle is **8% increase**.

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