Question

4. A piece of string is 120 cm long. What will be
the length of each side if the string is bent to form:
(i) a square
(ii) an equilateral triangle
(iii) a regular pentagon
(iv) a regular hexagon
side 60 m​

Answer 1

Answer:

(ilSide of square=30cm

(ii)Side of equilateral triangle=40cm

(iii)Side of pentagon=24cm

(iv)Side of hexagon=20cm

Step-by-step explanation:

(i) Size of string=120cm

We know,

perimeter of square=4×side

So,

4×side=120

=>Side=120/4

=>Side=30cm

So the side of square will be 30cm.

(ii) We know,

perimeter of equilateral triangle=3×side

So,

3×Side=120

=>Side=120/3

=>Side=40cm

So the side of an equilateral triangle will be 40 cm.

(iii)We know,

perimeter of a regular pentagon=5×Side

So,

5×side=120

=>Side=120/5

=>Side=24cm

So the side of a regular Pentagon will we 24cm.

(iv) We know,

perimeter of a regular hexagon=6×side

So,

6×side=120

=>Side=120/6

=>Side=20cm

So the side of a regular hexagon will be 20cm.

I hope it will help you :)

Answer 2

Before, finding the answer. Let's find out on how we can find the answer.

• Here, they have asked us to find the length of each side if the string is bent to many shapes.
• So, we have to divide the length of string by the number of sides of the shapes.

____________________

Given :

• Length of String = 120 cm

⇒ Shapes :

• a square
• an equilateral triangle
• a regular pentagon
• a regular hexagon

To find :

• each side if the string is bent to form shapes

Solution :

(i) a square :

${\sf Each \: Side = \dfrac{length \: of \: string}{square} }$

$\sf = \dfrac{120}{4}$

$\sf = 30 cm$

∴ Hence, Each side of Square is 30 cm.

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(ii) an equilateral triangle :

${\sf Each \: Side= \dfrac{length \: of \: string}{Equilateral \: Triangle} }$

$\sf = \dfrac{120}{3}$

$\sf = 40 cm$

∴ Hence, Each side of an Equilateral Triangle is 40 cm.

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(iii) a regular pentagon :

${\sf Each \: Side= \dfrac{length \: of \: string}{Pentagon} }$

              $\sf = \dfrac{120}{5}$

              $\sf = 24 cm$

∴ Hence, Each side of a Regular Pentagon is 24 cm.

(iv) a regular hexagon :

${\sf Each \: Side= \dfrac{length \: of \: string}{Hexagon} }$

              $\sf = \dfrac{120}{6}$

              $\sf = 20 cm$

∴ Hence, Each side of a Regular Hexagon is 20 cm.