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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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