Question

perumeter of rectangle is equal to the perimeter of squareif the length and breath of the rectangle is 20 m and 10 m find the area of square​

Answer 1

$\sf Given \begin{cases} & \sf{Perimeter_{\:(rectangle)} = Perimeter_{\:(square)}} \\ & \sf{Length\:of\:rectangle = \bf{20\:m}} \\ & \sf{Breadth\:of\:rectangle = \bf{10\:m}} \end{cases}$

To find: Area of square?

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☯ Let's consider side of square be a cm.

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

$:\implies\sf Perimeter_{\:(rectangle)} = Perimeter_{\:(square)}\\ \\ \\ :\implies\sf 2(length + breadth) = 4 \times side\\ \\ \\ :\implies\sf 2(20 + 10) = 4 \times a\\ \\ \\ :\implies\sf 2 \times 30 = 4 \times a\\ \\ \\ :\implies\sf 60 = 4 \times a \\ \\ \\ :\implies\sf a = \cancel{ \dfrac{60}{4}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{a = 15}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Side\:of\:square\:is\: {\textsf{\textbf{15\:m}}}.}}}$

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$\bf{\dag}\;{\underline{\frak{Now,\:Finding\:area\:of\:square,}}}$

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

$:\implies\sf Area_{\;(square)} = a \times a\\ \\ \\ :\implies\sf Area_{\;(square)} = 15 \times 15\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{Area_{\;(square)} = 225\:m^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Area\:of\:square\:is\: \bf{225\:m^2}.}}}$

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

• $\sf Perimeter\:of\:rectangle = \bf{2(length + breadth)}$

• $\sf Area\:of\:rectangle = \bf{length \times breadth}$

• $\sf Diagonal\:of\:rectangle = \bf{\sqrt{(length)^2 + (breadth)^2}}$

• $\sf Perimeter\:of\:square = \bf{4 \times side}$

• $\sf Diagonal\:of\:square = \bf{ \sqrt{2} \times side}$

Answer 2

Answer:

the area of the square is cm 225 cm^2 by putting 2(l+b)=4×side

Step-by-step explanation:

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