The length and the breadth of a rectangle are changed by +20% and by –10%, respectively. What is the percentage change in the area of the rectangle?

To solve this problem, we need to understand that the area of a rectangle is calculated by multiplying its length by its breadth.

Step 1: Let's assume the original length of the rectangle is 100 units and the original breadth is 100 units. Therefore, the original area is 100 * 100 = 10,000 square units.

Step 2: According to the problem, the length is increased by 20% and the breadth is decreased by 10%. So, the new length is 100 + 20% of 100 = 120 units and the new breadth is 100 - 10% of 100 = 90 units.

Step 3: The new area of the rectangle is now 120 * 90 = 10,800 square units.

Step 4: To find the percentage change in the area, we subtract the original area from the new area, divide by the original area, and then multiply by 100.

So, the percentage change in the area is ((10,800 - 10,000) / 10,000) * 100 = 8%.

Therefore, the percentage change in the area of the rectangle is an increase of 8%.