Question

17. The perimeter of a square and the circumference of a circle are equal. If the length
of each side of the square is 22 cm, find :
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.
​

Answer 1

$\sf\underbrace{Question:}$

The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find :

i). perimeter of the square.

$\sf{\underline{\underline{Answer:-}}}$

Given,

⇝ Side = 22cm

We know that,

$\bf{\underline\green{Perimeter \: of \: square \: = \: 4 \: × \: Side}}$

• Substitute the values,

⇝Perimeter = 4 × 22

${\bold\blue{Perimeter}}$ = 88cm

⠀

(ii) circumference of the circle.

$\sf{\underline{\underline{Answer:-}}}$

ATQ,

• The perimeter of square and the circumference of a circle are equal.

So,

⇝ perimeter of square = Circumference of circle

88cm = 88cm

${\bold\blue{Circumference}}$ = 88cm.

⠀

(iii) radius of the circle.

$\sf{\underline{\underline{Answer:-}}}$

We know that,

Circumference = $\huge\bf{\underline\green{2\pi \: r}}$

Substitute the Values,

(We have Circumference as 88cm.)

$88 = 2 \times \frac{22}{7} \times r$

$88 = \frac{44}{7} \times r$

$88 \times 7 = 44 \times r$

$616 = 44 \times r$

⇝radius = $\sf{\cancel\dfrac{616}{44}}$ = 14

${\bold\blue{Radius}}$ = 14cm.

Answer 2

(i) Side = 22 cm

Perimeter = 4 x side

= 4 x 22 = 88 cm

(ii) Circumference of circle

Given, Perimeter of square = Circumference

= 88 cm

(iii) Circumference = 88 cm

∴ Radius = C/2π

= 88×7/ 2x 22

= 66/ 44

=14 cm.

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