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If the length of a rectangle is doubled and the width is halved, how does the ar
If the length of a rectangle is doubled and the width is halved, how does the area change?
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Practice Questions
1 question
Q1
If the length of a rectangle is doubled and the width is halved, how does the area change?
Remains the same
Doubles
Halves
Quadruples
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Copy
New area = (2 × length) × (width/2) = length × width = original area. Area doubles.
Questions & Step-by-step Solutions
1 item
Q
Q: If the length of a rectangle is doubled and the width is halved, how does the area change?
Solution:
New area = (2 × length) × (width/2) = length × width = original area. Area doubles.
Steps: 9
Show Steps
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.
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