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15 October, 20:45

The length of a rectangle is 7 cm than 6 times its width. It's area is 10 square centimeters. Find the dimensions

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  1. 15 October, 23:28
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    So legnth is 7 more than 6 times width

    l=7+6w

    area=10 cm^2

    lw=area

    subsitute

    7+6w for l

    (7+6w) (w) = 10

    7w+6w^2=10

    subtract 10 from both sides

    6w^2+7w-10=0

    factor

    multiply 6 and - 10

    get - 60

    now find what 2 numbers multiply to get - 60 and add to get 7

    the answe ris - 5 and 12

    split up 7w into that

    6w^2+7w-10=0

    6w^2+12w-5w-10=0

    group

    (6w^2+12w) + (-5w-10) = 0

    undistribute factors

    (6w) (w+2) + (-5) (w+2) = 0

    reverse distribute (ab+ac=a (b+c)

    (w+2) ((6w) + (-5)) = 0

    (w+2) (6w-5) = 0

    set each to zero

    w+2=0

    subtract 2

    w=-2

    false, legnths cannot be negative

    6w-5=0

    add 5

    6w=5

    divide both sides by 6

    w=5/6

    subsitute

    l=7+6w

    l=7+6 (5/6)

    l=7+5

    l=12

    legnth=12 cm

    width=5/6 cm
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