Question

area of rectangle after increasing length and width

Answer 1

To find the area of a rectangle after increasing its length and width, you can follow these steps:

1. **Original Dimensions**: Let's denote the original length of the rectangle as \( L \) and the original width as \( W \).

2. **Increased Dimensions**: Assume the length is increased by \( \Delta L \) and the width is increased by \( \Delta W \). Therefore, the new length \( L' \) and new width \( W' \) can be expressed as:
\[
L' = L + \Delta L
\]
\[
W' = W + \Delta W
\]

3. **New Area**: The area \( A' \) of the rectangle after the increases will be:
\[
A' = L' \times W' = (L + \Delta L) \times (W + \Delta W)
\]

4. **Expanding the Area**: You can expand this expression as follows:
\[
A' = L \times W + L \times \Delta W + W \times \Delta L + \Delta L \times \Delta W
\]

Here, \( A = L \times W \) is the original area of the rectangle.

So the new area is the original area plus additional terms that account for the increases in length and width.

If you have specific values for \( L \), \( W \), \( \Delta L \), and \( \Delta W \), you can substitute them into the formula to find the new area.