Question

the area of a square field is 12544m².a rectangular field whose lengh is 24 more than its breadth and it's perimeter is equal to the perimeter of square find area of rectangular field​

Answer 1

Given:

• Area of square field is 12544 m².
• Length of Rectangular field is 24 m more than its breadth.
• $\sf Perimeter_{\;(rectangular\;field)} = Perimeter_{\;(square\;field)}$

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To find:

• Area of rectangular field?

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Solution:

⠀⠀

☯ Let breadth of Rectangular field be x m.

Therefore, Length of Rectangular field will be (x + 24) m

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

• Area of square field is 12544 m².

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

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

$:\implies\sf side \times side = 12544$

$:\implies\sf (side)^2 = 12544$

$:\implies\sf \sqrt{side^2} = \sqrt{12544}$

$:\implies{\underline{\boxed{\frak{\purple{side = 112\;m}}}}}\;\bigstar$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Now, Perimeter of square field,

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

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

$:\implies\sf Perimeter_{\;(square\:field)} = 4 \times 112$

$:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\;(square\:field)} = 448\;m}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\; Perimeter\;of\;square\;field\;is\; \bf{448\;m}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Given that,

⠀⠀

• $\sf Perimeter_{\;(rectangular\;field)} = Perimeter_{\;(square\;field)}$

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Therefore,

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

$\sf Here \begin{cases} & \sf{Length,\;l = \bf{x\;m}} \\ & \sf{Breadth,\;b = \bf{(x + 24)\;m}} \\ & \sf{Perimeter = \bf{448\;m}} \end{cases}$

$\dag\;{\underline{\frak{Putting\;values,}}}$

$:\implies\sf 2[x + (x + 24)] = 448$

$:\implies\sf x + (x + 24) = \cancel{ \dfrac{448}{2}}$

$:\implies\sf x + (x + 24) = 224$

$:\implies\sf 2x + 24 = 224$

$:\implies\sf 2x = 224 - 24$

$:\implies\sf 2x = 200$

$:\implies\sf x = \cancel{ \dfrac{200}{2}}$

$:\implies{\underline{\boxed{\frak{\purple{x = 100\;m}}}}}\;\bigstar$

Therefore,

⠀⠀

• Breadth of rectangle, x = 100 m
• Length of rectangle, (x + 24) = 124 m

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$\therefore$ Hence, Length and Breadth of Rectangular field is 100 m and 124 m respectively.

Answer 2

$\star\underline{\mathtt\orange{❥Q} \mathfrak\blue{u }\mathfrak\blue{E} \mathbb\purple{ s}\mathtt\orange{T} \mathbb\pink{iOn}}\star\:$

the area of a square field is 12544m².a rectangular field whose lengh is 24 more than its breadth and it's perimeter is equal to the perimeter of square find area of rectangular field

$\star\underbrace{\mathtt\red{❥ᴀ} \mathtt\green{n }\mathtt\blue{S} \mathtt\purple{W}\mathtt\orange{e} \mathtt\pink{R}}\star\:$

${ { \underbrace{ \mathbb{ \red{GiVeN\ }}}}}$

$Area\: of\: square\: field \:is\: 12544 m².$

$Length\: of \:Rectangular\: field\: is\: 24 m\\ more \:than \:its\: breadth.$

$\sf Perimeter_{\;(rectangular\;field)} = Perimeter_{\;(square\;field)}$

${ { \underbrace{ \mathbb{ \red{To\:PrOvE\ }}}}}$

$Area \:of\: rectangular\: field$

${ \color{aqua}{ \underbrace{ \underline{ \color{lime}{ \mathbb{\star SoLuTiOn\star }}}}}}$

$Let\: breadth \:of \:Rectangular\: field\: be\: xm.$

$Therefore\:Length\: of\: Rectangular\\ field\: will \:be \:(x + 24) m$

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

$Area \:of \:square \:field \:is \:12544 m².$

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

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

$\begin{gathered}:\implies\sf side \times side = 12544\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf (side)^2 = 12544\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf \sqrt{side^2} = \sqrt{12544}\\ \\\end{gathered}$

$:\implies{\underline{\boxed{\frak{\purple{side = 112\;m}}}}}\;\bigstar$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

$Now\: Perimeter\: of\: square\: field$

⠀⠀

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

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

$\begin{gathered}:\implies\sf Perimeter_{\;(square\:field)} = 4 \times 112\\ \\\end{gathered}$

$\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\;(square\:field)} = 448\;m}}}}}\;\bigstar\\ \\\end{gathered}$

$\therefore\;{\underline{\sf{Thus,\; Perimeter\;of\;square\;field\;is\; \bf{448\;m}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

$Given\: that$

⠀⠀

$\sf Perimeter_{\;(rectangular\;field)} = Perimeter_{\;(square\;field)}$

$Therefore$

$\begin{gathered}\star\;{\boxed{\sf{\pink{Perimeter_{\;(rectangle)} = 2(length + breadth)}}}}\\ \\\end{gathered}$

$\begin{gathered}\sf Here \begin{cases} & \sf{Length,\;l = \bf{x\;m}} \\ & \sf{Breadth,\;b = \bf{(x + 24)\;m}} \\ & \sf{Perimeter = \bf{448\;m}} \end{cases}\\ \\\end{gathered}$

$\begin{gathered}\dag\;{\underline{\frak{Putting\;values,}}}\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf 2[x + (x + 24)] = 448\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf x + (x + 24) = \cancel{ \dfrac{448}{2}}\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf x + (x + 24) = 224\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf 2x + 24 = 224\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf 2x = 224 - 24\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf 2x = 200\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf x = \cancel{ \dfrac{200}{2}}\\ \\\end{gathered}$

$\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{x = 100\;m}}}}}\;\bigstar\\ \\\end{gathered}$

$\therefore Breadth \:of\: rectangle\: x = 100 m$

$\therefore Length\: of\: rectangle \:(x + 24) = 124 m$

⠀⠀

$\therefore Hence\: Length \:and \:Breadth\: of\: Rectangular\\ field\: is\: 100 m \:and 124 m\: respectively.$