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The total area of a rectangle and a circle is 3970 cm2. The radius of the circle is equal to the semi perimeter of the triangle. The perimeter of the triangle is 70 cm and the length of the rectangle is 3/7th of the radius of the circle.  Then, what is the ratio of the perimeter of the rectangle to the perimeter of the circle?

The total area of a rectangle and a circle is 3970 cm2. The radius of the circle is equal to the semi perimeter of the triangle. The perimeter of the triangle is 70 cm and the length of the rectangle is 3/7th of the radius of the circle.  Then, what is the ratio of the perimeter of the rectangle to the perimeter of the circle? Correct Answer 23 : 110

Given:

Total area of a rectangle and a circle = 3970 cm2

Radius of the circle = Semi perimeter of the triangle

Perimeter of the triangle = 70 cm

Length of the rectangle = 3/7th × Radius of the circle

Formula Used:

Area of rectangle = length × breadth

Area of circle = πr2

Perimeter of the rectangle = 2(length + breadth)

Perimeter of circle = 2πr

Semi perimeter = (Perimeter of the triangle)/2

Calculation:

Perimeter of triangle = 70 cm

Radius of the circle = 70/2 = 35 cm

Area of the circle = π × 35 × 35

⇒ 22/7 × 35 × 35

⇒ 3850 sq. cm

∴ Length of the rectangle = 3/7 × 35 = 15 cm

Suppose the breadth of the rectangle is y cm.

⇒ 3850 + 15y = 3970

⇒ 15y = 3970 – 3850

⇒ 15y = 120

⇒ y = 120/15

⇒ y = 8 cm

Perimeter of the circle = 2 × 22/7 × 35

⇒ 220 cm

Perimeter of the rectangle = 2(15 + 8)

⇒ 2 × 23

⇒ 46 cm

∴ Required ratio = 46 : 220

⇒ 23 : 110

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