Question

Given: A circle with circumference 100 cm and a square inscribed in it.
Find the length of the side of this square.​

Answer 1

hope this helped u

506 is the approximate value

Answer 2

Given data:-

• A circle with circumference 100 cm and a square inscribed in it.

Solution:-

Let, quadrilateral ABCD is a inscribed square.

{We need to find radius ( r ) of circle}

→ Perimeter of circle = 2πr

{From given}

→ 100 = 2 × 22/7 × r

→ 100 = 44/7 × r i.e.

→ r = {100 × 7}/44

→ r = 700/44

→ r = 175/11

→ r = 50.9090 cm (approx)

According to figure AC is diameter.

AO & OC are radius of circle.

We know,

→ Diameter = 2 × radius

→ Diameter = 2 × 15.9090

→ Diameter = 31.818 cm

::Properties of square::

• All side of square are equal in length.
• All angle of square are equal to 90° or they are called as right angle
• Diameter = 31.818 cm of circle is know to be hypotenuse of square according to fingure and Properties of square.
• According to property we can assime that → DC = BC = x

Now, we use Pythagoras theorem to find side of square, so, now from figure

→ (AD)² = (DC)² + (BC)²

→ (31.818)² = (x)² + (x)²

→ 1012.3851 = 2x² i.e.

→ x² = 1012.3851/2

→ x² = 506.1925

→ x = √506.1925

→ x = 22.4987 cm

Hence, the length of side of square is 22.4987 cm.