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The perimeter of a rectangular field is fourth times of the perimeter of a square field. The ratio of the length of the rectangular field to the side of the square field is 6:1 and the diagonal of the square is 5√2 cm. Then, the area of the square field is what percentage of the area of the rectangular field?

The perimeter of a rectangular field is fourth times of the perimeter of a square field. The ratio of the length of the rectangular field to the side of the square field is 6:1 and the diagonal of the square is 5√2 cm. Then, the area of the square field is what percentage of the area of the rectangular field? Correct Answer 8.33%

Given:

Perimeter of a rectangular field = 4 × Perimeter of a square field

Ratio of length of rectangular field to side of square field = 6: 1

Diagonal of the square = 5√2 cm

Formula Used:

Perimeter of rectangular field = 2(length + breadth)

Area of rectangular field = length × breadth

Area of square = 4 × Side

Diagonal of square = √2 × side

Perimeter of square = 4 × Side of square

Calculation:

Diagonal of the square = 5√2 cm

Side of the square = 5 cm

Ratio of length of rectangular field to side of square field = 6: 1

∴ The length of the rectangular field = 30 cm

Perimeter of the square = 4 × 5 = 20 cm

∴ Perimeter of the rectangle = 4 × 20 = 80 cm

Suppose the breadth of the rectangle is x cm.

⇒ 2 × (x + 30) = 80

⇒ x + 30 = 40

⇒ x = (40 – 30)

⇒ x = 10 cm

Area of square = (5 × 5) = 25 sq. cm

Area of the rectangle = (10 × 30) = 300 sq. cm

∴ Required % = (25/300) × 100

⇒ 8.33%

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