Question

the perimeter of a rectangular field is 80 m and its area is 400 m², find the length and breadth of the field

please give it correct..​

Answer 1

${\underline{\boxed{\frak{\pmb{Length = 20 m, Breadth = 20 m}}}}}$

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❍ Let the Length of the rectangular field be x m.

$\underline{\bigstar\:\textsf{Let's Head to the Question Now :}}$

$:\implies\sf Perimeter = 2(Length + Breadth) = 80\\\\\\:\implies\sf (Length + Breadth) = \cancel\dfrac{80}{2} \\\\\\:\implies\sf x + b = 40 \\\\\\:\implies\sf b = 40 - x \qquad\quad \qquad\bigg\lgroup\bf Equation \;(I)\bigg\rgroup$

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A R E A:

$:\implies\sf Area of{rectangle} = Length \times Breadth \\\\\\:\implies\sf x \times (40 - x) = 400\\\\\\:\implies\sf 40x - x^2 = 400\\\\\\:\implies\sf x^2 - 40x + 400 = 0 \\\\\\:\implies\sf x^2 - 20x - 20x + 400 = 0\\\\\\:\implies\sf x(x - 20) -20(x - 20) = 0\\\\\\:\implies\sf (x - 20)^2 = 0\\\\\\:\implies\sf x - 20 = 0 \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 20\;m}}}}}\;\bigstar$

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$\underline{\bf{\dag} \:\mathfrak{By \; using \; Equation\;(1)\: :}}$⠀⠀⠀⠀

$:\implies\sf b = 40 - x \\\\\\:\implies\sf b = 40 - 20\\\\\\:\implies\sf{\underline{\boxed{\frak{\pink{b = 20 \;m}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \;length \; and \; Breadth \; of \; field \; are\; \bf{20m\;\&\;20m}.}}}$

Answer 2

Let the breadth of the rectangle be x metres,

then perimeter=82m

⇒2(Length+Breadth)=82

⇒Length+x=41

⇒Length=41−xmetres

Now, Area=400m^2

⇒Length×Breadth=400⇒(41−x)x=400

⇒41x−x^2 =400⇒x^2−41x+400=0⇒x^2

−25x−16x+400=0⇒(x−25)(x−16)=0

⇒x=25orx=16

Hence, breadth =25m or 16m