Question

The area of a square is 256 sq cm .Find
1) the length of each side of the square
2) the perimeter of the square.

Answer 1

Answer:

1) 16cm

2) 64cm

Step-by-step explanation:

1) Area of the square = S x S

= S x S = 256

= √256

= 16cm

Therefore length of each side of square = 16cm

2) Perimeter of square = 4S

= 4(16)

= 64 cm

Answer 2

Given: Area of square is 256 cm².

To find: Length of each sides and Perimeter of square.

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☯ Let length of each side be x cm.

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$\setlength{\unitlength}{2.2mm}\begin{picture}(10,10)\linethickness{0.5mm}\put(6,2){\dashbox{0.01}(15,15)}\put(3,0){\bf D}\put(3,18){\bf A}\put(23,18){\bf B}\put(23,0){\bf C}\put(23,9){\bf x cm}\put(11,0){\bf x cm}\put(8,9){\footnotesize\bf Area = 256 cm^2 }\end{picture}$

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$\bf{\dag}\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(square)} = side \times side}}}}$

$:\implies\sf x \times x = 256$

$:\implies\sf x^2 = 256$

$:\implies\sf \sqrt{x^2} = \sqrt{256}\qquad\qquad\bigg\lgroup\bf Taking\:sqrt.\:both\:sides \bigg\rgroup$

$:\implies{\underline{\boxed{\frak{\purple{x = 16\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Length\:of\:each\:side\:of\: square\:is\: {\textsf{\textbf{16\:cm}}}.}}}$

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$\bf{\dag}\;{\underline{\frak{Finding\: Perimeter\:of\:square,}}}$

$\star\;{\boxed{\sf{\pink{Perimeter_{\;(square)} = 4 \times side}}}}$

$:\implies\sf Perimeter_{\;(square)} = 4 \times x$

$:\implies\sf Perimeter_{\;(square)} = 4 \times 16\qquad\qquad\bigg\lgroup\bf x = 16\:cm \bigg\rgroup$

$:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\;(square)} = 64\:cm}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Perimeter\:of\: square\:is\: {\textsf{\textbf{64\:cm}}}.}}}$