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:

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

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

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

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

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

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

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Now, Perimeter of square field,

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

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

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

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

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

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Given that,

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

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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,

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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.