Question

find the length of the side of a square whose area is equal to the area of a rectangle having a length and breadth of 2.5 m and 0.9 m respectively​

Answer 1

Given:

Length of rectangle, l = 2.5 m

Breadth of rectangle, b = 0.9 m

$\sf Area_{\;(rectangle)} = Area_{\;(square)}$

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To find:

Length of side of square?

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Solution:

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

$\star\;{\boxed{\sf{\pink{Area_{\;(rectangle)} = length \times breadth}}}}$

$\sf Here \begin{cases} & \sf{Length,\;l = \bf{2.5\;m}} \\ & \sf{Breadth,\;b = \bf{0.9\;m}} \end{cases}$

$:\implies\sf Area_{\;(rectangle)} = 2.5 \times 0.9\\ \\ :\implies{\underline{\boxed{\frak{\purple{Area_{\;(rectangle)} = 2.25\;m^2}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\;Area\;of\;rectangle\;is\; \bf{2.25\;m^2}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

$:\implies\sf Area_{\;(rectangle)} = Area_{\;(square)}$

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

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

Therefore,

⠀⠀

$:\implies\sf Side \times Side = 2.25$

$:\implies\sf (side)^2 = 2.25$

$:\implies\sf \sqrt{(side)^2} = \sqrt{2.25}$

$:\implies{\underline{\boxed{\frak{\purple{Side = 2.25\;m}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Side\;of\;square\;is\; \bf{1.5\;m}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}$

Perimeter of Rectangle = 2(length + breadth)

Perimeter of square = 4 × side

Diagonal of square = √2 × side

Diagonal of rectangle = √(length)² + (breadth)²

Answer 2

$\huge\mathcal{\mid{\mid{\underline{\green{Good\: Afternoon\:}}}{\mid{\mid}}}}$

Qᴜᴇsᴛɪᴏɴ ;-

✔️ Find the length of the side of a square whose area is equal to the area of a rectangle having a length and breadth of 2.5 m and 0.9 m respectively.

$\huge{\orange{\boxed{\fcolorbox{lime}{indigo}{\color{aqua}ANSWER}}}}$

$\Large\bf\pink{GiVeN,}$

• $\bf\red{Length\:of\: Rectangle}$ = 2.5 cm

• $\bf\red{Breadth\:of\: Rectangle}$ = 0.9 cm

$\Large\bf\blue{We\: know\: that,}$

$\red\bigstar\:\:\bf\green{Area\:of\: Rectangle\:=\: Length\:\times\: Breadth}$

$\bold\longmapsto\:\rm{Area\:of\: Rectangle\:=\:2.5\:\times\:{0.9}}$

$\bold\longmapsto\:\bf\orange{Area\:of\: Rectangle\:=\:2.25\:cm^2}$

$\bf\gray{According\:to\:the\: question,}$

$\pink\bigstar\:\:\bf{\color{indigo}{Area\:of\: Square\:=\: Area\:of\: Rectangle}}$

$\bold\longmapsto\:\:\rm{Area\:of\: Square\:=\:2.25\:cm^2}$

$\bold\longmapsto\:\:\rm{Side\:\times\:{Side}\:=\:2.25\:cm^2}$

$\bold\longmapsto\:\:\rm{(Side)^2\:=\:2.25\:cm^2}$

$\bold\longmapsto\:\:\rm{Side\:=\:\sqrt{2.25\:cm^2}}$

$\bold\longmapsto\:\:\bf\green{Side\:=\:1.5\:cm}$

$\Large\bold\therefore$ The length of the side of a square is 1.5 cm.