Question

A steel wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent in the form of a circle, then the circumference of the circle is​

Answer 1

• GIVEN:-

1. A steel wire when bent in the form of a square encloses an area of 121 cm².
2. The same wire is bent in the form of a circle.

• TO FIND:-

circumference of the circle.

• SOLUTION:-

Area of square = 121 sq. cm

We know that

Area of square = side × side

According to the question,

$\large\Longrightarrow{\sf{area={side}^{2}}}$

$\large\Longrightarrow{\sf{121={side}^{2}}}$

By square rooting both sides,

$\large\Longrightarrow{\sf{\sqrt{121}=side}}$

$\large\therefore\boxed{\sf{side=\frac{+}{-}11}}$

Now,

The perimeter of square = 4 × side.

= 4 × 11

= 44 cm.

It is said that wire is bent in the form of a circle.

So,

Perimeter of square = circumference or perimeter of circle

=> 44 cm = 44 cm.

$\large\orange\therefore\boxed{\bf{\orange{Circumference\:of\:the\:circle\:is\:44\:cm.}}}$