https://file.aiquickdraw.com/mathbot/file/1726298222344a3ys2o4i.jpg

The question in the image is in Bengali and translates to:

"If the length of a rectangle is increased by 10% and the width is decreased by 10%, what is the percentage change in the area of the rectangle?"

### Solution:

Let the original length be \( L \) and the original width be \( W \). Then, the original area \( A_1 \) is:
\[
A_1 = L \times W
\]

When the length is increased by 10%, the new length becomes:
\[
L' = L \times 1.10
\]
And when the width is decreased by 10%, the new width becomes:
\[
W' = W \times 0.90
\]

Now, the new area \( A_2 \) is:
\[
A_2 = L' \times W' = (L \times 1.10) \times (W \times 0.90)
\]
\[
A_2 = L \times W \times 1.10 \times 0.90 = A_1 \times (1.10 \times 0.90)
\]
\[
A_2 = A_1 \times 0.99
\]

So, the new area is 99% of the original area, meaning there is a 1% decrease in the area of the rectangle.

### Answer: The area decreases by 1%.

Would you like more details or have any questions?

Here are 5 related questions to further expand on this concept:
1. What happens if both the length and width of a rectangle are increased by 10%?
2. How would the result change if the length increases by 15% and the width decreases by 10%?
3. Can you derive a formula for the percentage change in area when both dimensions change by different percentages?
4. How is the area affected when both the length and width of a rectangle decrease by the same percentage?
5. What would be the impact on the area if one dimension remains unchanged and the other is altered by a percentage?

#### Tip:
When calculating percentage changes involving products (like area), a small percentage increase and decrease in two factors does not cancel out but leads to a combined effect that should be carefully calculated.

একটি আয়তক্ষেত্রের দৈর্ঘ্য 10% বাড়ালে এবং প্রস্থ 10% কমালে আয়তক্ষেত্রের ক্ষেত্রফলের শতকরা কী পরিবর্তন হয়?

Find out how a 10% increase in the length and a 10% decrease in the width of a rectangle affects its area. This problem involves calculating the percentage change in area using geometric concepts.

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