Question

A piece of string is 30 cm long. What will be the length of each side if the string
is used to form :​

Answer 1

Given:

• A piece of string = 30cm.

To Find:

• Length of each side if string is used to form a square = ?

Diagram:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 7.5\ cm}\put(4.4,2){\bf\large 7.5\ cm}\end{picture}$

Solution:

We know that;

$\star \: \boxed{\mathfrak\gray{Perimeter \: of \: square = 4a}}$

Substituting values,

$:\implies\mathfrak{perimeter \: of \: square = 30} \\ \\ :\implies\mathfrak{4a = 30} \\ \\ \\ :\implies\mathfrak{a = \dfrac{\cancel{30}}{\cancel{4}}} \\ \\ \\:\implies\mathfrak{a = 7.5} \\ \\ \\ \mathfrak{:\implies{\underline{\boxed{\mathfrak{a = 7.5cm}}}}}$

Hence,

• Length of each side of square will be 7.5cm.

Verification:

$:\implies\mathfrak{perimeter \: of \: square = 4a} \\ \\ \\ :\implies\mathfrak{perimeter \: of \: square \: =4 \times 7.5} \\ \\ \\ :\implies\mathfrak{perimeter \: of \: square \: =30} \\ \\ \\ \mathfrak{:\implies{\underline{\boxed{\mathfrak{Perimeter \: of \: square = 30cm}}}}}$

Answer 2

$\large{\underbrace{\sf{\red{Appropriate\:Question:}}}}$

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.

$\large{\boxed{\sf{\pink{How\:to\:solve\:this\:question?}}}}$

Here, we are asked to find the length of each side of the square if the string is used to form the square.As it given in the question that the length of the string is 30cm long so the perimeter or the length of the boundary of square is also 30cm long.We will use the formulae of perimeter of the square and find the length of each side of the square.

So, Let's do it!

$\large{\underbrace{\sf{\blue{Acknowledgement:}}}}$

${\boxed{\sf{\orange{Perimeter\:of\:the\:square=4a\: where\:a\:is\:the\:length\:of\:each\:side}}}}$

$\huge{\underbrace{\sf{\purple{Solutíon:}}}}$

$\implies{\sf{4a=30}}$

$\implies{\sf{a= \dfrac{30}{4}}}$

$\implies{\sf{a= \dfrac{30}{4}}}$

$\implies{\sf{a= \dfrac{15}{2}=7.5cm}}$

$\large\implies{\boxed{\sf{a=7.5cm}}}$

Hence, the length of each side of the square is 7.5cm long.

And we are done! :D

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