Question

A rectangle whose length and breath is 18m and 8m respectively has to be converted to a square with same area. What will be the side of the square?​

Answer 1

Given :

• Length and Breadth of a Rectangle is 18 m and 8 m respectively .

To Find :

• Side of square if the area of rectangle is equal to the area of Sqaure .

Solution :

Firstly we'll find the Area of Rectangle :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}$

Putting Values :

$\longmapsto\tt{18\times{8}}$

$\longmapsto\tt\bf{144\:{m}^{2}}$

Now ,

As Given that the Area of Rectangle is equal to the Area of Square . So ,

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Square={(Side)}^{2}}$

Putting Values :

$\longmapsto\tt{144={(Side)}^{2}}$

$\longmapsto\tt{\sqrt{144}=Side}$

$\longmapsto\tt\bf{12\:m}$

So , The Side of Square is 12 m .

Answer 2

• $\Large\boxed{\sf{\blue{Side\:of\:square\:=\:\bf{12\:m}}}}$

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$\underline{\underline{\bf{\red{Given\::-}}}}$

• Length of the rectangle = 18 m
• Breadth of the rectangle = 8 m
• Rectangle is converted into square with same area.

$\underline{\underline{\bf{\red{To\:Find\::-}}}}$

• Side of square = ?

$\underline{\underline{\bf{\red{Solution\::-}}}}$

★ Finding area of rectangle :-

$\bf\dag\:\bigg\lgroup \sf{Area\:of\:rectangle = Length\:\times\:Breadth}\bigg\rgroup$

$\quad\longrightarrow\quad\sf Area\:of\:rectangle = 18\:\times\:8$

$\quad\longrightarrow\quad\bf{ Area\:of\:rectangle = \pink{144\:m^2}}$

Now,

★ According to the question :-

$\quad\longrightarrow\quad\sf Area\:of\:square = Area\:of\:rectangle$

$\quad\bf\dag\:\bigg\lgroup \sf{Area\:of\:square = (Side)^2}\bigg\rgroup$

$\quad\longrightarrow\quad\sf (Side)^2 = 144$

$\quad\longrightarrow\quad\sf Side = \sqrt{144}$

$\quad\longrightarrow\quad\sf Side = \sqrt{\underline{12\:\times\:12}}$

$\quad\longrightarrow\quad\bf{Side = \purple{12\:m}}$

$\small\therefore\:{\underline{\sf{Hence,\:side\:of\:square\:is\: \bf{12\:m}\:\sf{respectively.}}}}$

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