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The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm.
Quantity I: Area of Square
Quantity II:Area of Rectangle
Quantity II:Area of Rectangle
- a)Quantity I > Quantity II
- b)Quantity I < Quantity II
- c)Quantity I ≥ Quantity II
- d)Quantity I ≤ Quantity II
- e)Quantity I = Quantity II or relation cannot be established
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The perimeter of a rectangle and a square is 160 cm each. If the diffe...
Perimeter of rectangle = Perimeter of Square = 160
4a = 160 ⇒ a = 40
Area of square = 1600
1600 – lb = 600
lb = 1000 cm²
4a = 160 ⇒ a = 40
Area of square = 1600
1600 – lb = 600
lb = 1000 cm²
Most Upvoted Answer
The perimeter of a rectangle and a square is 160 cm each. If the diffe...
Perimeter of Square and Rectangle:
- Let the side of the square be x cm. Therefore, the perimeter of the square is 4x cm.
- Let the length and breadth of the rectangle be l cm and b cm respectively. Therefore, the perimeter of the rectangle is 2(l+b) cm.
Given:
- Perimeter of Square = Perimeter of Rectangle = 160 cm
- Difference between areas of square and rectangle = 600 cm
Calculations:
- From the given information, we can write:
4x = 160
x = 40 cm
2(l+b) = 160
l + b = 80
Area of Square:
- Area of square = x^2 = 40^2 = 1600 cm^2
Area of Rectangle:
- Area of rectangle = l*b
- Substitute l + b = 80 into the equation:
l*(80-l) = 1600
80l - l^2 = 1600
l^2 - 80l + 1600 = 0
(l-40)^2 = 0
l = 40 cm, b = 40 cm
Area of rectangle = 40*40 = 1600 cm^2
Comparison:
- Quantity I (Area of Square) = 1600 cm^2
- Quantity II (Area of Rectangle) = 1600 cm^2
Therefore, Quantity I is equal to Quantity II. Hence, the correct answer is option 'A' (Quantity I = Quantity II).
- Let the side of the square be x cm. Therefore, the perimeter of the square is 4x cm.
- Let the length and breadth of the rectangle be l cm and b cm respectively. Therefore, the perimeter of the rectangle is 2(l+b) cm.
Given:
- Perimeter of Square = Perimeter of Rectangle = 160 cm
- Difference between areas of square and rectangle = 600 cm
Calculations:
- From the given information, we can write:
4x = 160
x = 40 cm
2(l+b) = 160
l + b = 80
Area of Square:
- Area of square = x^2 = 40^2 = 1600 cm^2
Area of Rectangle:
- Area of rectangle = l*b
- Substitute l + b = 80 into the equation:
l*(80-l) = 1600
80l - l^2 = 1600
l^2 - 80l + 1600 = 0
(l-40)^2 = 0
l = 40 cm, b = 40 cm
Area of rectangle = 40*40 = 1600 cm^2
Comparison:
- Quantity I (Area of Square) = 1600 cm^2
- Quantity II (Area of Rectangle) = 1600 cm^2
Therefore, Quantity I is equal to Quantity II. Hence, the correct answer is option 'A' (Quantity I = Quantity II).
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The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm.Quantity I: Area of SquareQuantity II:Area of Rectanglea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'A'. Can you explain this answer?
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The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm.Quantity I: Area of SquareQuantity II:Area of Rectanglea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm.Quantity I: Area of SquareQuantity II:Area of Rectanglea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm.Quantity I: Area of SquareQuantity II:Area of Rectanglea)Quantity I > Quantity IIb)Quantity I < Quantity IIc)Quantity I ≥ Quantity IId)Quantity I ≤ Quantity IIe)Quantity I = Quantity II or relation cannot be establishedCorrect answer is option 'A'. Can you explain this answer?.
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