Question

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

Answer 1

Answer:

l = b = 20m

Step-by-step explanation:

2(l + b) = 80

l + b = 40

l = 40 - b

lb = 400

b(40 - b) = 400

40b - b^2 = 400

b^2 - 40b + 400 = 0

We will now factorise it.

b^2 - 20b - 20b + 400 = 0

b(b - 20) - 20(b - 20) = 0

(b - 20) (b - 20) = 0

(b - 20)^2 = 0

b - 20 = 0

b = 20 m

l = 40 - b = 40 - 20 m = 20m

Answer 2

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

━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠀

$\rule{250}2$

A R E A :

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

⠀⠀⠀

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

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

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