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If a square and rhombus have same perimeter, and area of square is S and area of rhombus is R, then
- a)S > R
- b)R > S
- c)R = S
- d)data insufficient
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a square and rhombus have same perimeter, and area of square is S a...
Area of square = a2
Area of rhombus = a2 sin θ
∵ sin θ < 1
∴ a2 > a2 sin θ
ar (square) > ar (rhombus)
⇒ S > R
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Community Answer
If a square and rhombus have same perimeter, and area of square is S a...
Explanation:
Perimeter of Square and Rhombus:
- Let the side length of the square be 'a' and the side length of the rhombus be 'b'.
- Since the perimeter of a square is 4a and the perimeter of a rhombus is 4b, given that they have the same perimeter, we have 4a = 4b.
Area of Square and Rhombus:
- The area of a square is given by S = a^2.
- The area of a rhombus is given by R = (1/2) x (diagonal 1) x (diagonal 2).
Comparing Areas:
- For the square, S = a^2.
- For the rhombus, R = (1/2) x (diagonal 1) x (diagonal 2) < (1/2)="" x="" (2a)="" x="" (2a)="" />
Conclusion:
- Since 2a^2 > a^2, we can conclude that the area of the rhombus (R) is greater than the area of the square (S) when they have the same perimeter.
- Therefore, the correct answer is option 'A' - S > R.
Perimeter of Square and Rhombus:
- Let the side length of the square be 'a' and the side length of the rhombus be 'b'.
- Since the perimeter of a square is 4a and the perimeter of a rhombus is 4b, given that they have the same perimeter, we have 4a = 4b.
Area of Square and Rhombus:
- The area of a square is given by S = a^2.
- The area of a rhombus is given by R = (1/2) x (diagonal 1) x (diagonal 2).
Comparing Areas:
- For the square, S = a^2.
- For the rhombus, R = (1/2) x (diagonal 1) x (diagonal 2) < (1/2)="" x="" (2a)="" x="" (2a)="" />
Conclusion:
- Since 2a^2 > a^2, we can conclude that the area of the rhombus (R) is greater than the area of the square (S) when they have the same perimeter.
- Therefore, the correct answer is option 'A' - S > R.
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If a square and rhombus have same perimeter, and area of square is S and area of rhombus is R, thena)S > Rb)R > Sc)R = Sd)data insufficientCorrect answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If a square and rhombus have same perimeter, and area of square is S and area of rhombus is R, thena)S > Rb)R > Sc)R = Sd)data insufficientCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a square and rhombus have same perimeter, and area of square is S and area of rhombus is R, thena)S > Rb)R > Sc)R = Sd)data insufficientCorrect answer is option 'A'. Can you explain this answer?.
If a square and rhombus have same perimeter, and area of square is S and area of rhombus is R, thena)S > Rb)R > Sc)R = Sd)data insufficientCorrect answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If a square and rhombus have same perimeter, and area of square is S and area of rhombus is R, thena)S > Rb)R > Sc)R = Sd)data insufficientCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a square and rhombus have same perimeter, and area of square is S and area of rhombus is R, thena)S > Rb)R > Sc)R = Sd)data insufficientCorrect answer is option 'A'. Can you explain this answer?.
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