If the length of a rectangle is doubled and the width is halved, how does the area change?
Correct Answer: Area remains the same.
- Step 1: Understand the formula for the area of a rectangle, which is Area = Length × Width.
- Step 2: Let the original length be L and the original width be W.
- Step 3: Calculate the original area using the formula: Original Area = L × W.
- Step 4: Now, double the length: New Length = 2 × L.
- Step 5: Now, halve the width: New Width = W / 2.
- Step 6: Calculate the new area using the new dimensions: New Area = (2 × L) × (W / 2).
- Step 7: Simplify the new area: New Area = (2L × W) / 2 = L × W.
- Step 8: Compare the new area to the original area: New Area = Original Area.
- Step 9: Conclude that the area does not change; it remains the same.
- Area of a Rectangle – Understanding how to calculate the area of a rectangle using the formula Area = length × width.
- Effect of Dimensional Changes – Analyzing how changes in dimensions (length and width) affect the overall area.
