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If the length and breadth of a rectangle are doubled how does its perimeter change?
- a)Doubled
- b)Tripled
- c)Halved
- d)Remains the same
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the length and breadth of a rectangle are doubled how does its peri...
Explanation:
To understand how the perimeter of a rectangle changes when its length and breadth are doubled, let's break it down step by step.
Original Rectangle:
- Let the original length of the rectangle be L units.
- Let the original breadth of the rectangle be B units.
- The original perimeter of the rectangle = 2(L + B) units.
Doubled Length and Breadth:
- When the length and breadth of the rectangle are doubled:
- New length = 2L units
- New breadth = 2B units
New Perimeter:
- The new perimeter of the rectangle = 2(2L + 2B) units
- Simplifying the expression, we get:
= 2(2L + 2B)
= 2*2(L + B)
= 4(L + B) units
Comparison:
- Original perimeter = 2(L + B) units
- New perimeter = 4(L + B) units
Conclusion:
- The new perimeter of the rectangle is 4 times the original perimeter when the length and breadth are doubled. Therefore, the perimeter changes by a factor of 4, which means it is tripled.
This explains why the correct answer is option 'A' - Tripled.
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