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

Question

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

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Amara 1 month 2021-08-13T02:53:00+00:00 1 Answer 0 views 0

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    2021-08-13T02:54:12+00:00

    \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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