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Consider the following figure and answer the item that follows A square is divided into four rectangles as shown above. The lengths of the sides of rectangles are natural numbers. The areas of two rectangles are indicated in the figure. What is the length of each side of the square ?

Consider the following figure and answer the item that follows A square is divided into four rectangles as shown above. The lengths of the sides of rectangles are natural numbers. The areas of two rectangles are indicated in the figure. What is the length of each side of the square ? Correct Answer 11

Calculation:

Area of ABIH = 15

⇒ AH = 3 and AB = 5

Now, Area of EFID = 48

Possibilities of length and breadth are - (1,48), (2,24), (3,16), (4,12), (6,8)

Since BC > AB

⇒ BC > 5

Now, BD = ID

⇒ BC = ID = 6

Hence, Length of square = 11

∴  The length of each side of the square is 11

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