Question

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Answer 1

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

Need to find: Area of square?

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

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

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

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

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

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

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

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

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

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

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