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If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.
- a)6%
- b)4%
- c)5%
- d)9%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the sides of a rectangle are increased by 5%, find the percentage i...
According to the formula,
Percentage increase in diagonals = 5%
Percentage increase in diagonals = 5%
Most Upvoted Answer
If the sides of a rectangle are increased by 5%, find the percentage i...
Understanding the Problem
To find the percentage increase in the diagonals of a rectangle when its sides are increased by 5%, we start by recalling the formula for the diagonal of a rectangle. The diagonal (d) can be calculated using the Pythagorean theorem:
d = √(length² + width²)
Initial Dimensions
- Let the initial length of the rectangle be L.
- Let the initial width of the rectangle be W.
Increased Dimensions
- After a 5% increase:
- New length, L' = L + 0.05L = 1.05L
- New width, W' = W + 0.05W = 1.05W
Calculating the Initial Diagonal
- Initial diagonal, d = √(L² + W²)
Calculating the New Diagonal
- New diagonal, d' = √((1.05L)² + (1.05W)²)
- Simplifying this, we get:
- d' = √(1.1025L² + 1.1025W²)
- d' = √(1.1025(L² + W²)) = 1.05√(L² + W²)
- Thus, d' = 1.05d
Percentage Increase in Diagonal
- The increase in diagonal = d' - d = 1.05d - d = 0.05d
- Percentage increase = (Increase / Original) × 100
- Percentage increase = (0.05d / d) × 100 = 5%
Conclusion
The percentage increase in the diagonals of the rectangle is 5%. Thus, the correct answer is option C.
To find the percentage increase in the diagonals of a rectangle when its sides are increased by 5%, we start by recalling the formula for the diagonal of a rectangle. The diagonal (d) can be calculated using the Pythagorean theorem:
d = √(length² + width²)
Initial Dimensions
- Let the initial length of the rectangle be L.
- Let the initial width of the rectangle be W.
Increased Dimensions
- After a 5% increase:
- New length, L' = L + 0.05L = 1.05L
- New width, W' = W + 0.05W = 1.05W
Calculating the Initial Diagonal
- Initial diagonal, d = √(L² + W²)
Calculating the New Diagonal
- New diagonal, d' = √((1.05L)² + (1.05W)²)
- Simplifying this, we get:
- d' = √(1.1025L² + 1.1025W²)
- d' = √(1.1025(L² + W²)) = 1.05√(L² + W²)
- Thus, d' = 1.05d
Percentage Increase in Diagonal
- The increase in diagonal = d' - d = 1.05d - d = 0.05d
- Percentage increase = (Increase / Original) × 100
- Percentage increase = (0.05d / d) × 100 = 5%
Conclusion
The percentage increase in the diagonals of the rectangle is 5%. Thus, the correct answer is option C.
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If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.a)6%b)4%c)5%d)9%Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.a)6%b)4%c)5%d)9%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.a)6%b)4%c)5%d)9%Correct answer is option 'C'. Can you explain this answer?.
If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.a)6%b)4%c)5%d)9%Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.a)6%b)4%c)5%d)9%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sides of a rectangle are increased by 5%, find the percentage increase in its diagonals.a)6%b)4%c)5%d)9%Correct answer is option 'C'. Can you explain this answer?.
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