Question

the area of a square field is 5184m². a rectangular field whose length is twice the breadth, has its perimeter equal to the perimeter of the square field. find the area of the rectangular field ?

Answer 1

Let the side of square be x

Area of square=x^2

5184m^2=x^2

x=72 m


perimeter of square field=4 x

4×72
288 m


Let the length be 2x and breadth=x


Perimeter of square field =perimeter of rectangular field


Perimeter of rectangular field=2 (l+b)

288=2 (2x+x)

288=4x+2x

288=6x

288/6=x


48=x.


Length of rectangular field=2×48=96m

Breadth of rectangular field=48m


Area of rectangular field=96×48=4608m^2


Hence the area of rectangular field is 4608m^2.



hope its helps

Answer 2

Given:

• Area of square field is 5184 m².
• Length of Rectangular field is twice its breadth.
• $\sf Perimeter_{\;(rectangular\;field)} = Perimeter_{\;(square\;field)}$

⠀⠀

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 "2x" m

⠀⠀

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

Area of square field is 5184 m².

⠀⠀

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

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

$:\implies\sf side \times side = 5184$

$:\implies\sf (side)^2 = 5184$

$:\implies\sf \sqrt{side^2} = \sqrt{5184}$

$:\implies{\underline{\boxed{\frak{\purple{side = 72\;m}}}}}\;\bigstar$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Now, Perimeter of square field,

⠀⠀

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

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

$:\implies\sf Perimeter_{\;(square\:field)} = 4 \times 72$

$:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\;(square\:field)} = 288\;m}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\; Perimeter\;of\;square\;field\;is\; \bf{288\;m}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Given that,

⠀⠀

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

⠀⠀

Therefore,

⠀⠀

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

$\sf Here \begin{cases} & \sf{Length,\;l = \bf{2x\;m}} \\ & \sf{Breadth,\;b = \bf{x\;m}} \\ & \sf{Perimeter = \bf{288\;m}} \end{cases}$

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

$:\implies\sf 2[(2x + x)] = 288$

$:\implies\sf 4x + 2x = 288$

$:\implies\sf 6x = 288$

$:\implies\sf x = {\cancel \dfrac {288}{6}}$

$:\implies\sf x = 48$

$:\implies{\underline{\boxed{\frak{\purple{x = 48\;m}}}}}\;\bigstar$

Therefore,

⠀⠀

• Breadth of rectangle, x = 48 m
• Length of rectangle, 2x = 2 × x = 96 m

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

Now, Area of rectangular field,

⠀⠀

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

$\star\;{\boxed{\sf{\pink{Area_{\;(rectangle)} = Length \times Breadth}}}}$

$\sf:\implies{Area_{\;(rectangle)} = 96 \times 48}$

$:\implies{\underline{\boxed{\frak{\purple{Area_{\;(rectangular \:field)} = 4608\;m^2}}}}}\;\bigstar$

$\therefore$ Hence, the area of the rectangular field is 4608 m²