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The ratio of the area of the circle, square and rectangle is 154: 100: 75, respectively. The length of the rectangle is 5 cm more than the breadth of it. If the perimeter of the rectangle is 70 cm, then, perimeter of square is what percentage of the perimeter of the circle (in approximate)?

The ratio of the area of the circle, square and rectangle is 154: 100: 75, respectively. The length of the rectangle is 5 cm more than the breadth of it. If the perimeter of the rectangle is 70 cm, then, perimeter of square is what percentage of the perimeter of the circle (in approximate)? Correct Answer 90.90%

Given:

Ratio of the area of the circle, square and rectangle = 154: 100: 75

Length of rectangle = breadth of rectangle + 5 cm

Perimeter of rectangle = 70 cm

Formula Used:

Area of the circle = πr2

Area of square = side × side

Area of rectangle = length × breadth

Perimeter of rectangle = 2(length + breadth)

Calculation:

Perimeter of rectangle = 70 cm

Suppose breadth of rectangle is x cm

Then, length of rectangle will be (x + 5)

So, Perimeter = 2(x + x + 5) = 70

⇒ 2x + 5 = 35

⇒ 2x = 30

⇒ x = 15 cm

Breadth of rectangle is 15 cm

Length of rectangle will be 20 cm

Area of the rectangle = (15× 20) = 300 sq. cm

The ratio of the area of the circle, square and rectangle is 154: 100: 75, respectively.

⇒ 75 units = 300

⇒ 1 unit = 4

⇒ 154 units = 616

⇒ 100 units = 400

The Area of the circle = 616

⇒ πr2 = 616

⇒ 22/7 × r2 = 616

⇒ r2 = 196

⇒ r = √196

⇒ r = 14 cm

Perimeter of circle = 2 × 22/7 × 14

⇒ 88 cm

Area of square = 400 sq. cm

Side of square = 20 cm

Perimeter of square = 4 × 20 = 80 cm

∴ required % = 80/88 × 100

⇒ 90.90%

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