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

Step-by-step explanation:

Step-by-step explanation:

Given length and breadth of rectangle is 13.6 m and 3.4 m respectively.

we know formula for area of rectangle .

Area of rectangle = length × breadth .

putting values here

Area of rectangle = 13.6 m × 3.4 m

Area of rectangle = 46.24 m^2m

2

Also given in question.

Area of rectangle = Area of square.

Area of square = side × side

\begin{gathered}\large \text{$a^2=46.24$}\\\\\\\large \text{$a=\sqrt{46.24}$}\\\\\\\large \text{$a=6.8 \ m$}\\\\\\\end{gathered}

a

2

=46.24

a=

46.24

a=6.8 m

So length of each side of a square is 6.8 m

Let side of square be a m

Answer 2

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