If the length of a rectangle is doubled and the width is halved, how does the ar

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Question: If the length of a rectangle is doubled and the width is halved, how does the area change?

Options:

Correct Answer: Doubles

Solution:

New area = (2 × length) × (width/2) = length × width = original area. Area doubles.

If the length of a rectangle is doubled and the width is halved, how does the area change?

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.