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Perimeters of a rectangle and a square are equal. Perimeter of the square is 96 cm and breadth of the rectangle is 4 cm less than the side of the square. Then two times the area (in square cm) of the rectangle is
1. 560
2. 960
3. 1040
4. 1120

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Correct Answer - Option 4 : 1120

Given:

Perimeters of a rectangle = Perimeter of a square

Perimeter of square = 96 cm

Breadth of rectangle = Side of square - 4

Formula used:

Perimeter of rectangle = 2 × (Length + Breadth)

Perimeter of square = 4 × Side of square 

Area of rectangle = Length × Width 

Calculations:

Let the side of square be x and the length of rectangle be L

Perimeter of square = 4x 

⇒ 4x = 96

⇒ x = 24 cm

Breadth of rectangle = 24 - 4

⇒ 20 cm

Perimeter of rectangle = 2 × (L + 20) 

⇒ 2 × (L + 20) = 96

⇒ L + 20 = 48

⇒ L = 28 cm

Area of the rectangle = 28 × 20

⇒ 560 cm2

∴ Two times the area of the rectangle is = 2 × 560 = 1120 cm2

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