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The diagonal of a square is the length of a rectangle and the area of a rectangle is 96 cm2. The breadth of a rectangle is 8 cm then, find the perimeter of the square.
1. 18√2 
2. 32
3. 24√2 
4. 24

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Correct Answer - Option 3 : 24√2 

Given:

Area of a rectangle = 96 cm2

Breadth of a rectangle = 8 cm 

Formula used:

Area of a rectangle = length × breadth 

The perimeter of a square = 4 × side

Diagonal of a square = side × √2 

Calculations:

Length of a rectangle be 'x'

Area of a rectangle = x × 8

⇒ 96 = 8 × x

⇒ x = 96 ÷ 8

⇒ x = 12 cm

Diagonal of a square is length of rectangle

√2 × side = 12

Side of a square = 12/√2

 Perimter of a side = 4 × (12/√2)

⇒ 24√2 cm  

∴ The perimeter of a square is 24√2  cm 

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