Question

the length and the breadth of a rectangle are 40 cm and 10cm respectively find the perimeter of a square of area equal to that of the rectangle​

Answer 1

Given:

• Length of Rectangle = 40 cm
• Breadth of rectangle = 10 cm
• $\sf Area_{\;(square)} = Area_{\;(rectangle)}$

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To find:

• Perimeter of square?

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☯ Let side of square be x cm.

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

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

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We know that,

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• $\sf Area_{\;(square)} = (side)^2$

• $\sf Area_{\;(Rectangle)} = length \times breadth$

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Therefore,

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$:\implies\sf side \times side = length \times breadth$

$:\implies\sf x \times x = 40 \times 10$

$:\implies\sf x^2 = 400$

$:\implies\sf \sqrt{x^2} = \sqrt{400}\qquad\quad\bigg\lgroup\bf Squaring\;both\;sides \bigg\rgroup$

$:\implies{\underline{\boxed{\frak{\purple{x = 20}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Side\;of\;square\;is\;{\textsf{\textbf{20\;cm}}}.}}}$

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Now, Finding Perimeter of square,

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

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

$:\implies\sf Perimeter_{\;(square)} = 4 \times 20$

$:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\;(square)} = 80\;cm}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Perimeter\;of\;square\;is\;{\textsf{\textbf{80\;cm}}}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:Formulas\:related\:to\:it\:\bigstar}}}}$

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Area\ formula&\bf Perimeter\ formula\\\cline{1-3}\sf Square&\tt side \times side}&\tt 4 \times side\\\cline{1-3}\sf Rectangle&\tt length \times breadth&\tt 2(length + breadth)\\\cline{1-3}\sf Triangle&\tt \dfrac{1}{2} \times base \times height&\tt sum\of\ all\ sides\ of\ \triangle\\\cline{1-3}\end{array}$