Question

The circumference of a semicircle is 125cm if the diameter of the semicircle

Answer 1

$\huge\mathtt\pink{140 √2 cm}$

Given:

The circumference of a semi-circle is 125 cm

The diameter of the semi-circle is 30% less than the diagonal of the square.

Formula:

Circumference of the semi-circle = πr + 2r

Perimeter of the square = 4a

Diagonal of the square = √2 a

Calculation:

According to the question,

According to the question,πr + 2r = 126 cm

⇒ r (22/7 + 2) = 126

⇒ r × (36/7) = 126

⇒ r = 126 × (7/36)

⇒ r = 49/2 cm

Diameter of the semi-circle = 2 × 49/2 = 49 cm

According to the question

Diameter of the semi-circle = 70% of the diagonal of the square.

⇒ 49 = 70/100 × √2a

49 = 70/100 × √2a⇒ a = 49 × 100/70√2

a = 49 × 100/70√2⇒ a = 35√2 cm

∴ Perimeter of the square = 4 × 35√2 = 140√2 cm