Question

Find the area of square that has the same perimeter as arectangle whose length and breadth are 18cm and 8cm respectively​

Answer 1

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have given that length and breadth of a Rectangle which having the same perimeter as perimeter of square. Then, we have to find the area of square.

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Here, f1stly we will find the perimeter of Rectangle then placing it equal to the formula of Perimeter of square we will find the side of the square. Then, we will apply the formula for area of square then substituting the value we will get the area of square which is our required.

Let's Do It ⚡

$\huge{\underline{\boxed{\sf AnSwer}}}$

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Given:-

• Perimeter of Rectangle = Perimeter of square
• Length = 18cm
• Breadth = 8cm

Find:-

• Area of square.

Solution:-

Here, we know that

$\: \: :\implies \: \: \underline{\boxed{\sf Perimeter_{Rectangle} = 2(l+b)}}$

$\sf where \small{\begin{cases} \sf l = 18cm \\ \sf b = 8cm\end{cases}}$

$\footnotesize{\underline{\underline{\mathcal{ \bigstar SUBSTITUTING \: THESE \: VALUES:}}}}$

$:\Longrightarrow\sf Perimeter_{Rectangle} = 2(l+b)$

$:\Longrightarrow\sf Perimeter_{Rectangle} = 2(18+8)$

$:\Longrightarrow\sf Perimeter_{Rectangle} = 2(26)$

$:\Longrightarrow\sf Perimeter_{Rectangle} = 2 \times 26$

$:\Longrightarrow\sf Perimeter_{Rectangle} = 52cm$

Now,

$\underline{\underline{\mathcal{ \bigstar According \: To \: Question:}}}$

$\sf\Longrightarrow Perimeter_{Rectangle} = Perimeter_{Square}$

And,

$\: \: :\implies \: \: \underline{\boxed{\sf Perimeter_{square} = 4(side)}}$

So,

$\sf\Longrightarrow 52= 4(side)$

$\sf\Longrightarrow \dfrac{52}{4}= side$

$\sf\Longrightarrow 13cm= side$

So, the side of the square is 13cm

Now, using

$\: \: :\implies \: \: \underline{\boxed{\sf Area_{square} = side \times side}}$

$\sf where \small{\begin{cases} \sf side = 13cm\end{cases}}$

$\underline{\underline{\mathcal{ \bigstar Substituting \: The\: Value:}}}$

$\dashrightarrow\sf Area_{square} = side \times side$

$\dashrightarrow\sf Area_{square} = 13 \times 13$

$\dashrightarrow\sf Area_{square} = 169 {cm}^{2}$

$\underline{\boxed{\sf \therefore Area \:of\:the\:square\: is\:169cm^2}}$

Answer 2

$\sf Given \begin{cases} & \sf{Length\;of\;rectangle = \bf{18\;cm}} \\ & \sf{Breadth\;of\;rectangle = \bf{8\;cm}} \\ & \sf{Perimeter_{\;(square)} = Perimeter_{\;(rectangle)}} \end{cases}$

Need to find: Area of square?

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

$\star\;{\boxed{\sf{\purple{Perimeter_{\;(rectangle)} = 2(length + breadth)}}}}$

$:\implies\sf Perimeter_{\;(rectangle)} = 2(18 + 8)$

$:\implies\sf Perimeter_{\;(rectangle)} = 2 \times 26$

$:\implies{\boxed{\sf{\pink{Perimeter_{\;(rectangle)} = 52\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\; Perimeter\;of\;rectangle\;is\; \bf{52\;cm}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━

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

• Perimeter of square = Perimeter of Rectangle

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☯ Let side of square be x cm.

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Therefore,

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$\star\;{\boxed{\sf{\purple{Perimeter_{\;(square)} = 4 \times side}}}}$

$:\implies\sf 4 \times x = 52$

$:\implies\sf x = \cancel{ \dfrac{52}{4}}$

$:\implies{\boxed{\sf{\pink{x = 13\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\;side\;of\;square\;is\; \bf{13\;cm}.}}}$

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Now, Finding Area of square,

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

$:\implies\sf Area_{\;(square)} = 13 \times 13$

$:\implies{\boxed{\sf{\pink{Area_{\;(square)} = 169\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\;square\;is\; \bf{169\;cm^2}.}}}$