Question

a piece of string is 30 cm long what will be the length of each side if the string is used to form a square and equilateral triangle and a regular hexagon​

Answer 1

$\huge\underbrace\red{Answer}$

Given :-

➢ A piece of string is 30cm long( perimeter)

To Find :-

➢ Length of each side if the string is used to form

• Square

• Equilateral triangle

• Regular hexagon

Solution :-

❖ Square :-

Let the side of square be x

We know that,

Perimeter of square = 4 × side

By substituting values,

➙ 30cm = 4 × x

➙ 30cm = 4x

➙ 30/4 = x

➠ 7.5cm = x

Hence, The Length of each side if the string is used to form Square will be 7.5cm

❖ Equilateral triangle

Let the side of equilateral triangle be x

we know that,

Perimeter of equilateral triangle = 3 × side

By substituting values,

➙ 30cm = 3 × x

➙ 30cm = 3x

➙ 30/3 = x

➠ 10cm = x

Hence, The Length of each side if the string is used to form Equilateral triangle will be 10cm

❖ Regular Hexagon

Let the side of regular hexagon be x

we know that,

Perimeter of regular hexagon = 6 × side

By substituting values,

➙ 30cm = 6 × side

➙ 30cm = 6 × x

➙ 30cm = 6x

➙ 30/6 = x

➠ 5cm = x

Hence, The Length of each side if the string is used to form Regular Hexagon will be 5cm

Answer 2

$\huge\underbrace{\pink{\bf{❖SoluTion:}}}$

Given,

Length of piece of String = 30cm

ψSquare:

Now, The Piece of String was mould into a Square

Number of sides of Square = 4

☆ $\boxed{\sf{Perimeter\;of\; Square = 4s}}$

☆ $\boxed{\sf{Side\;of\; Square = \frac{4s}{4}}}$

$→\;{\bf{Side = \frac{30}{4}}}$

$→\;{\bf{Side = 7.5cm}}$

☞ Length of each side of String when moulded into a Square

◕➜ $\Large\fbox\red{\tt{7.5cm}}$

________________________________

ψEquilateral Triangle:

Now, The string was moulded into an Equilateral Triangle

Number of sides of Equilateral Triangle = 3

☆ $\boxed{\sf{Perimeter\;of\; Equilateral\; Triangle = 3s}}$

☆ $\boxed{\sf{Side\;of\; Equilateral\; Triangle = \frac{3s}{3}}}$

$→\;{\bf{Side = \frac{30}{3}}}$

$→\;{\bf{Side = 10cm}}$

☞ Length of each side of String when moulded into an Equilateral Triangle

◕➜ $\Large\fbox\green{\tt{10cm}}$

________________________________

ψRegular Hexagon:

Now, The string was moulded into a Regular Hexagon

Number of sides of Regular Hexagon = 6

☆ $\boxed{\sf{Perimeter\;of\; Regular\; Hexagon = 6s}}$

☆ $\boxed{\sf{Side\;of\; Regular\; Hexagon = \frac{6s}{6}}}$

$→\;{\bf{Side = \frac{30}{6}}}$

$→\;{\bf{Side = 5cm}}$

☞ Length of each side of String when moulded into a Regular Hexagon

◕➜ $\Large\fbox\orange{\tt{5cm}}$

Hope It Helps You ✌️