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?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀

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

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

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

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

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

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

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

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

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

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

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

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

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

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

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

Answer 2

Answer:

Given :-

• Perimeter of rectangle = Perimeter of square
• Length of rectangle = 20 m
• Breadth of rectangle = 10 m

To Find :-

Area of square

Solution :-

For finding area we will first find side of square

$\tt \implies \: Perimeter (rectangle) = Perimeter (square)$

$\tt \implies \: 2(l + b) = 4 \times s$

$\tt \implies 2(20 + 10) = 4s$

$\tt \implies \: 2(30) = 4s$

$\tt \implies \: 60 = 4s$

$\tt \implies \: s \: = \dfrac{60}{4}$

$\mathfrak \green{side = 15 \: m}$

Now,

Let's find Area of square

$\bf \: Area \:of \: square \: = {side}^{2}$

$\tt \implies \: Area = {15}^{2}$

$\tt \implies \: Area = 15 \times 15$

$\mathfrak \purple{Area = 225 \: {m}^{2} }$

Hence :-

$\dag \bf \underline {Area \: of \: square \: = 225 \: {m}^{2} }$