The width of a rectangle is only 15% of its length. If the perimeter of the rectangle is 46, what is the length

The width of a rectangle is only 15% of its length. If the perimeter of the rectangle is 46, what is the length

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  1. Answer:

    20 units

    Step-by-step explanation:

    Let the length be x. According to the question,

    • Length = x
    • Width = 15% of the length

    ➝ Width = 15% of the length

    ➝ Width = 15/100x

    Width = 3/20x

    We have the perimeter of the rectangle that is 46 units.

    [tex]\longrightarrow \sf {Perimeter_{(Rec.)} = 2(L + W) } \\ [/tex]

    [tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

    [tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

    [tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{20x + 3x}{20} \Bigg \rgroup } \\ [/tex]

    [tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{23x}{20} \Bigg \rgroup } \\ [/tex]

    [tex]\longrightarrow \sf {\dfrac{46}{2}= \dfrac{23x}{20}} \\ [/tex]

    [tex]\longrightarrow \sf {23= \dfrac{23x}{20}} \\ [/tex]

    [tex]\longrightarrow \sf {23 \times 20 = 23x} \\ [/tex]

    [tex]\longrightarrow \sf {460= 23x} \\ [/tex]

    [tex]\longrightarrow \sf {\cancel{\dfrac{460}{23}} = x} \\ [/tex]

    [tex]\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\ [/tex]

    Therefore, length of the rectangle is 20 units.

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