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In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 100% respectively, then its perimeter increases by
  • a)
    40/3%
  • b)
    20%
  • c)
    25%
  • d)
    27%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a rectangle, length is three times its breadth. If the length and t...
Let the breadth of the rectangle = x Length of the the rectangle will be = 3 times of breadth = 3x
So the initial perimeter = 2(length + breadth) = 2(x + 3x) = 8x
New breadth after increase = x + 10x/100 = 1.1x
New length after increase = 3x + 30*3x/100 = 3.9x
New perimeter = 2(1.1x + 3.9x) = 10x
Percentage change in perimeter = ( 10x-8x )*100/8x = 25%
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Most Upvoted Answer
In a rectangle, length is three times its breadth. If the length and t...
Given:
Length (L) = 3 × Breadth (B)

After increase:
New length = 1.3L
New breadth = 2B

To find:
Percentage increase in perimeter

Solution:
Let the original length and breadth of the rectangle be L and B respectively.

Perimeter of the rectangle = 2(L+B)

Original perimeter = 2(L+B)

New perimeter = 2(1.3L + 2B) = 2.6L + 4B

Percentage increase in perimeter = ((New perimeter - Original perimeter) / Original perimeter) × 100

=((2.6L + 4B - 2(L+B)) / 2(L+B)) × 100

=((2.6L + 4B - 2L - 2B) / 2(L+B)) × 100

=((0.6L + 2B) / (L+B)) × 100

Now, L = 3B

=((0.6 × 3B + 2B) / (3B + B)) × 100

=((3.8B) / 4B) × 100

=95%

Hence, the percentage increase in perimeter is 25% (option C).
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In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 100% respectively, then its perimeter increases bya)40/3%b)20%c)25%d)27%Correct answer is option 'C'. Can you explain this answer?
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