Question

* A rectangle is 81 m long and 36 m broad. Find the side of a square whose area is
equal to the area of this rectangle.​

Answer 1

Given

Sides of rectangle

length= 81m

Breadth= 36m

Area of rectangle= Area of square

To Find

We have to find out the side of square

Solution

first find the area of square

$\bullet\sf\ Area\ of\ square= (side)^2\\ \\ \bullet\sf\ Area\ of\ rectangle= length\times breadth\\ \\ \\ :\implies\sf\ (side)^2= \ell\times b\\ \\ \\ :\implies\sf\ \ (Side)^2= 81\times 36\\ \\ \\ :\implies\sf\ Side= \sqrt{81\times 36}\\ \\ \\ :\implies\sf\ Side= \sqrt{9\times 9\times 6\times 6}\\ \\ \\ :\implies\sf\ Side= 9\times 6\\ \\ \\ :\implies\sf\ Side= 54m\\ \\ \\ :\implies\underline{\boxed{\sf\ Side\ of\ square= 54m}}$

Verification:-

Area of square = Area of rectangle

→ 54×54= 81×36

→ 2916sq.m = 2916sq.m

LHS = RHS

Hence our answer is correct !

Answer 2

AnswEr-:

• $\underline {\dag{\mathrm {The \:Side\:of\:Square \:is\:\bf{54\:m}}}}$

Explanation-:

$\mathrm {\bf{ Given-:}}$

• The length of a rectangle is 81 m

• The Breadth of Rectangle is 36 m.

• Area of Rectangle is equal to Area of Square.

$\mathrm {\bf{ To\:Find -:}}$

• The Side of Square.

$\sf{\bf{\dag{ Solution \:of\:Question -:}}}$

$\underbrace {\mathrm { \bf{ Understanding \:of\:Concept \:-:}}}$

• We have to find the Length of Side of a square when the Area of Rectangle is equal to the Area of Square and the Length and Breadth of Rectangle is given .

• Firstly we have to find the area of Rectangle by Putting known Values [ Length and Breadth] in Formula for Area of Rectangle and it is give that Area of Rectangle is equal to the Area of Square.

• By Putting The area of Square in the Formula for Area of Square then ,

• We can get the side of Square.

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$\sf{\bf{\dag{Finding \:Area \:of\:Rectangle -:}}}$

As , We know that -:

• $\underline{\boxed{\mathrm{\pink {Area\:of\:Rectangle \:-: Length \: \times Breadth \:sq.units}}}}$

$\mathrm {\bf{ Here-:}}$

• The length of a rectangle is 81 m
• The Breadth of Rectangle is 36 m.

Now , By Putting known Values in Formula for Area of Rectangle-:

• $\longmapsto {\mathrm { Area\:-:81 \times 36 }}$

• $\longmapsto {\mathrm { Area\:-:2916 \:m^{2} }}$

Therefore,

• $\longmapsto {\mathrm { Area_{(Rectangle)}\:-:2916 \:m^{2} }}$

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As , We have given that ,

• Area of Rectangle is equal to Area of Square.

Then ,

• $\longmapsto {\mathrm { Area_{(Square)}\:-:2916 \:m^{2} }}$

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$\sf{\bf{\dag{Finding \:Side \:of\:Rectangle -:}}}$

As , We know that ,

• $\underline{\boxed{\mathrm{\pink {Area\:of\:Square \:-: Side \: \times Side \:or\:Side^{2}\:sq.units}}}}$

$\mathrm {\bf{ Here-:}}$

• Area of Square is 2916 m²

Now , By Putting known Values in Formula for Area of Square-:

• $\longmapsto {\mathrm { Side^{2}\:=2916 m^{2} }}$

• $\longmapsto {\mathrm { Side\:=\sqrt {2,916} }}$

As, We know that ,

• [ 54² = 2916 ]

• $\longmapsto {\mathrm { Side\:=54m }}$

Hence ,

• $\underline {\dag{\mathrm {The \:Side\:of\:Square \:is\:\bf{54\:m}}}}$

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