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The perimeter of a rectangle of length 12 cm and breadth 16 cm is equal to the perimeter of a square and a semicircle whose diameter is equal to the side of a square then find the circumference of a semicircle?

The perimeter of a rectangle of length 12 cm and breadth 16 cm is equal to the perimeter of a square and a semicircle whose diameter is equal to the side of a square then find the circumference of a semicircle? Correct Answer 36 cm

Given:

Length of rectangle = 12 cm

Breadth of rectangle = 16 cm

Condition:

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The perimeter of a rectangle is equal to the perimeter of the square.               ….. (1)

The diameter of the semicircle is equal to the side of the square.      ………… (2)

Formula:

Perimeter of a rectangle = 2 × (l + b)

The perimeter of a square = 4 × side

Circumference of semicircle = πr + 2r

Diameter of semicircle = 2d

Calculation:

Let the length of a rectangle be 'l' cm and the breadth of a rectangle be 'b' cm and

Let ‘a’ be the side of the square

Now,

Perimeter of a rectangle = 2 × (12 + 16)

⇒ 2 × 28

⇒ 56 cm

Now,

The perimeter of a square = 4 × a

⇒ 4a

Now,

By using the above condition (1)

⇒ 56 = 4a

⇒ a = 56/4

⇒ a = 14 cm

Now,

By using the above condition (2)

Diameter of semicircle = 14 cm

Now,

Circumference of semicircle = 22/7 × 14/2 + 2 × 7 

⇒ 22/7 × 7 + 14

⇒ 36 cm

∴ The circumference of the semicircle is 36 cm

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