Question

Is it possible to design a rectangular Park of perimeter 86 and area 410 metre square? If so find its length and breadth.​

Answer 1

$\sf \fbox \red{Question}$

• Is it possible to design a rectangular Park of perimeter 86 and area 410 metre square? If so find its length and breadth.

$\sf \fbox \red{Solution}$

$\bf \: = let \: lenght \: be \: x$

$\bf \: = Given \: that$

$\sf \: = 2(lenght + breadth) = 80m$

$\sf \: = (lenght \: + breadth) = \frac{80}{2}$

$\sf \: = (x + breadth) = 40$

$\sf \: = breadth \: = 40 - x$

$\bf \: also \: given \: that \: area \: = 400 {m}^{2}$

$\sf \: = lenght \: \times breadth \: = 400$

$\sf \: = x(40 - x) = 400$

$\sf \: = \: 40x - {x}^{2} = 400$

$\sf \: = 40x - {x}^{2} - 400 = 0$

$\sf \: = 0 = - 40x + {x}^{2} + 400 = 0$

$\sf \: = - 40x + {x}^{2} + 400 = 0$

$\sf \: = {x}^{2} - 40x + 400 = 0$

$\bf \: we \: factories \: by \: splitting \: the \: middle \: term \:$

$\bf \: splitting \: the \: middle \: term \: method \: \\ \bf \: we \: need \: to \: find \: two \: number \: whose \: \\ \bf \: sum \: = - 40 \\ \bf \: product \: = 400 \times 1 = 400$

$\sf \: = {x}^{2} - 20x - 20x + 400 = 0$

$\sf \: = x(x - 20) - 20(x - 20) = 0$

$\sf \: = (x - 20)(x - 20) = 0$

$\bf \: = \: so \: the \: root \: of \: the \: equation \: are \:$

$\sf \: = x - 20 = 0 \\ \sf \: x = 20$

$= \bf \fbox \red {so \: x = 20 \: is \: the \: solution}$

$\sf \: = lenght \: = x = 20m$

$\sf \: = breadth \: = 40 - x = 40 - 20 = 20m$

$\sf \: Answer \: = \fbox \red{20m}$

Answer 2

Answer:

no I don't think it's possible beacuse they are having irrational roots

Step-by-step explanation:

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