If the area of a rectangle is 53.6 cm², and the length is quadrupled while the width is halved, what will be the new area?

• A. 107.2 cm²
• B. 53.6 cm²
• C. 80.0 cm²
• D. 40.0 cm²

Answer: (A)

To determine the new area of the rectangle after the changes to the dimensions, we start with the relationship between the original area, length, and width. The original area, given as 53.6 cm², can be expressed as Area = Length × Width.

When the length is quadrupled, it means we are multiplying the original length by 4. If we denote the original length as L and the original width as W, the new length becomes 4L. Simultaneously, the width is halved, meaning the new width is W/2.

Now, we can find the new area using the modified dimensions:

New Area = New Length × New Width

New Area = (4L) × (W/2)

When we simplify this expression, we find:

New Area = 4L × (W/2) = (4L × W) / 2 = 2LW

Since the original area (LW) is 53.6 cm², we substitute that value into our equation:

New Area = 2 × 53.6 cm² = 107.2 cm².

In conclusion, by quadrupling the length and halving the width, the area effectively doubles, which results