1.

Area of a square is 8 times the area of a rectangle. Find the ratio of diagonal of the square to the diagonal of the rectangle, if the length of the rectangle is half the length of the side of the square.1. 1 : 2 2. 3√2 : 5√33. 4√2 : √5 4. √3 : √5

Answer» Correct Answer - Option 3 : 4√2 : √5 

Given :

Area of the square is 8 times the area of the rectangle

Length of rectangle is half the length of the side of the square

Formula Used :

Area of the square = side2

Area of the rectangle = length × breadth

Calculations :

Let the side of the square be ‘s’

Let the length of the rectangle be ‘l’ and breadth be ‘b’

According to the question

S2 = 8 × (I × b)

(2l)2 = 8 × (l × b)      (l = (s/2) or s = 2 l)

4 l2 = 8 × l × b

⇒ b = l/2

Now,

Diagonal of the square = √2 × side = √2s = 2√2 l     (s = 2l)

Diagonal of the rectangle = √[(l)2 + (b)2] = √[(l)2 + (l/2)2]

⇒ √[(5/4)(l)2]

⇒ (l/2)√5    

Diagonal of square : Diagonal of rectangle = 2√2l : (l/2)√5

⇒ 4√2 : √5

∴ The ratio of the diagonals is 4√2 : √5 


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