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The ratio of the perimeter of the rectangle to the diagonal of a square is 7 : √2. The side of square is 2 cm more than the breadth of the rectangle and 14 cm less than the length of the rectangle then what is the ratio between the area of rectangle to the area of square?

The ratio of the perimeter of the rectangle to the diagonal of a square is 7 : √2. The side of square is 2 cm more than the breadth of the rectangle and 14 cm less than the length of the rectangle then what is the ratio between the area of rectangle to the area of square? Correct Answer 33 : 16

Given:

Ratio of the perimeter of the rectangle to the diagonal of the square = 7 : √2

Side of the square = Breadth of the rectangle + 2 cm = Length of the rectangle – 14 cm

Formula Used:

Perimeter of rectangle = 2(length + breadth)

Diagonal of square = √2 × Side of square

Area of rectangle = (length × breadth)

Area of square = (side × side)

Calculation:

Suppose the side of the square is x cm.

Then, length of the rectangle will be (x + 14) cm and breadth of rectangle will be (x - 2) cm

Perimeter of the rectangle = 2(length + breadth)

⇒ 2(length + breadth)

⇒ 2(x - 2 + x + 14)

⇒ 2(2x + 12) cm

Diagonal of the square = √2x cm

According to question –

⇒ 2(2x + 12)/√2x = 7/√2

⇒ 4x + 24 = 7x

⇒ 3x = 24

⇒ x = 24/3

⇒ x = 8 cm

Length of rectangle = (8 + 14) = 22 cm

Breath of rectangle = (8 – 2) = 6 cm

Side of square = 8 cm

⇒ Area of the rectangle = (22 × 6) = 132 cm2

⇒ Area of the square= 8 × 8 = 64 cm2

∴ required ratio = 132 : 64

⇒ 33 : 16

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