Question

the length and breadth of a rectangular 9 metre and 49 metre respectively find the side of a square whose area is equal to the area of the rectangle also find the perimeter of a square​

Answer 1

Answer:

$\bold\green{Side\:of\:square}$ = $\small{\boxed{\bold{21\:m}}}$

$\bold\green{Perimeter\:of\:square}$ = $\small{\boxed{\bold{84\:m}}}$

Step-by-step explanation:

Given:-

• $\bold\red{Length = 9\:m}$
• $\bold\green{Breadth = 49\:m}$

$\bold{Area\:of\:rectangle = Area\:of\:square}$

• $\bold\red{Side\:of\:square=?}$
• $\bold\green{Perimeter\:of\:square=?}$

$\bigstar{\boxed{\bold{Area\:of\:rectangle = Length \times Breadth}}}$

$\Rightarrow\sf Area\:of\:rectangle =(9 \times 49)\:{m}^{2} \\\\\Rightarrow{\boxed{\sf\red{Area\:of\:rectangle = 441\:{m}^{2} }}}$

$\rule{300}{1}$

$\bigstar{\boxed{\bold{Area\:of\:square={(Side)}^{2} }}}$

$\Rightarrow\sf 441 = {(Side)}^{2} \\\\\Rightarrow\sf Side =\sqrt{441} \\\\\Rightarrow{\boxed{\bold\red{Side = 21\:m}}}$

$\therefore\bold{Side\:of\:square = 21\:m}$

$\rule{300}{1}$

$\bigstar{\boxed{\bold{Perimeter\:of\:square = 4 \times Side}}}$

$\Rightarrow\sf Perimeter\:of\:square = (4 \times 21)\:m \\\\\Rightarrow{\boxed{\bold\red{Perimeter\:of\:square = 84\:m}}}$

$\therefore\bold{Perimeter\:of\:square = 84\:m}$

Answer 2

ANSWER :

$\bf{\Large{\underline{\bf{Given\::}}}}$

The length and the breadth of a rectangular 9m & 49m respectively.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The side of the square whose area is equal of the rectangle & also find the perimeter of square.

$\bf{\Large{\underline{\tt{\red{Explanation\::}}}}}$

$\bf{We\:Have}\begin{cases}\sf{Length\:of\:rectangle\:=\:9m}\\ \sf{Breadth\:of\:rectangle\:=\:49m}\end{cases}}$

A/q

$\leadsto{\boxed{\sf{\pink{Area\:of\:square\:=\:Area\:of\:rectangle\:}}}}$

Let the side of square be R m

$\implies\sf{R*R\:=\:Length*Breadth}\\\\\\\\\implies\sf{R^{2} \:=\:(9*49)m^{2} }\\\\\\\\\implies\sf{R^{2} \:=\:441m^{2} }\\\\\\\\\implies\sf{R \:=\:\sqrt{441m^{2} } }\\\\\\\\\implies\sf{\red{R\:=\:21m}}$

So, the side of square is 21m.

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$\bf{\Large{\underline{\sf{\bigstar{The\:Perimeter\:of\:the\:Square\::}}}}}$

$\longmapsto\sf{Perimeter\:=\:4*side}$

$\longmapsto\sf{Perimeter\:=\:(4*21)m}$

$\longmapsto\sf{\red{Perimeter\:=\:84m}}$