Math, asked by peepeepoopoo76, 8 months ago

calculate the perimeter of a square whose area is
$49 {x}^{2} - 112x + 64$

Answers

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$
$\huge\boxed{\fcolorbox{red}{pink}{4(7x - 8)}}$
$\huge{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$
⚪ Area of the square $= 49 {x}^{2} - 112x + 64$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$
⚪ Perimeter of the square.

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$
⚪ Quadratic Equations
⚪ Squaring of variables

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$
✏ let a be the side of the square.

Therefore,
Area $= {a}^{2}$
$\Rightarrow 49 {x}^{2} - 112x + 64 = {a}^{2}$
$\Rightarrow {(7x)}^{2} - 2(7x)(8) + {(8)}^{2} = {a}^{2}$
$\Rightarrow {(7x - 8)}^{2} = {a}^{2}$ ——————— [ $\because {a}^{2} - 2ab + {b}^{2} = {(a - b)}^{2}$ ]
$\Rightarrow (7x - 8) = a$ ———————— [ square-rooting both the sides ]
$\Rightarrow a = 7x - 8$

✒ Hence,
perimeter of the square
$= 4a$
$= 4(7x - 8)$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$
⚪ Perimeter of the square = 4(7x - 8)

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calculate the perimeter of a square whose area is
$49 {x}^{2} - 112x + 64$