Increase in Length and Breadth:
Let's assume the original length of the rectangle is L and the original breadth is B. After increasing both by 15%, the new length will be 1.15L and the new breadth will be 1.15B.

Calculating the Area:
The area of a rectangle is given by the formula A = length × breadth. Therefore, the original area is A = L × B, and the new area is A' = (1.15L) × (1.15B).

Calculating the Percentage Increase:
To find the percentage increase in the area, we need to calculate the difference between the new area and the original area, and then express it as a percentage of the original area.

The difference between the new area and the original area is given by:
Difference = A' - A = (1.15L) × (1.15B) - L × B

To express the difference as a percentage of the original area, we divide the difference by the original area and multiply by 100:
Percentage Increase = (Difference / A) × 100

Simplifying the Expression:
Let's substitute the values of A' and A into the expression for the difference:
Difference = (1.15L) × (1.15B) - L × B
Difference = 1.3225LB - LB
Difference = 0.3225LB

Now, let's substitute the value of the difference into the expression for the percentage increase:
Percentage Increase = (0.3225LB / A) × 100

Since A = LB, we can simplify further:
Percentage Increase = (0.3225LB / LB) × 100
Percentage Increase = 0.3225 × 100
Percentage Increase = 32.25%

Conclusion:
Therefore, the area of the rectangle increases by 32.25% when both the length and the breadth are increased by 15%.

(1.15L)*(1.15B)=1.17lb
it means 17 % increase