the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths

the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths

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  1. Answer:

    Length of the rectangle:

    [tex]x = \frac{4800}{106} = \frac{2400}{53} [/tex]

    Breadth of the rectangle:

    [tex]60\%(x) = \frac{60}{100} \times \frac{4800}{106} \: \: \: \: \: \: \: \: \: \: \: \\ =60 \times \frac{48}{106} \\ = \frac{2880}{106} [/tex]

    Step-by-step explanation:

    Longer side of the rectangle(length) = x

    Shorter side of the rectangle(breadth) = (60%)x

    Perimeter of the rectangle = 2(l+b) = 96 inches

    Hence,

    [tex]96 = 2(x + 60\%(x))[/tex]

    [tex]96 = 2(x + \frac{6}{100 } x)[/tex]

    [tex]96 = 2( \frac{100}{1 00} x + \frac{6}{100} x)[/tex]

    [tex]96 = 2( \frac{106}{100} x)[/tex]

    [tex]96 = \frac{106}{50} x[/tex]

    [tex]96 \div \frac{106}{50} = x[/tex]

    [tex]96 \times \frac{50}{106} = x[/tex]

    [tex] \frac{4800}{106} = x[/tex]

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