Final answer:
The area of the rectangle increases by 43.75% when the length is increased by 15% and the breadth is increased by 25%. The percentage increase is calculated by multiplying the scale factors for the length and breadth, subtracting one, and then multiplying the result by 100%.
Step-by-step explanation:
The student is asking about the percentage increase in area of a rectangle when the rectangle's length and breadth are increased by 15% and 25%, respectively. To calculate this, we can start with the initial length L and breadth B of the rectangle. An increase of 15% in length L would be L × 1.15, and an increase of 25% in breadth B would be B × 1.25. The new area A' would be:
A' = (L × 1.15) × (B × 1.25)
This simplifies to:
A' = L × B × 1.15 × 1.25
The original area A is:
A = L × B
The percentage increase in area can be calculated as:
Percentage Increase = ((A' - A) / A) × 100%
By substituting A' and A:
Percentage Increase = (((L × B × 1.15 × 1.25) - (L × B)) / (L × B)) × 100%
This gives us:
Percentage Increase = (1.15 × 1.25 - 1) × 100% = 0.4375 × 100% = 43.75%
Therefore, the area of the rectangle increases by 43.75% when the length and breadth are increased by 15% and 25%, respectively.