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27 November, 16:42

The length of a rectangle is 9 centimeters more than the width. the area is 112 square centimeters. find the length and width of the rectangle

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Answers (2)
  1. 27 November, 18:25
    0
    Here,

    let width (b) be x then,

    length (l) = 9cm+x

    area = 112 sq cm

    now,

    area of rectangle=l*b

    or, 112 = (9+x) x

    or, 112=9x+x^2

    or, 0=x^2+9x-112

    or, 0=x^2 + (16-7) x-112

    or, 0=x^2+16x-7x-112

    or, 0=x (x+16) - 7 (x+16)

    or, 0 = (x-7) (x+16)

    either,

    0=x-7

    or, 7=x

    x=7cm

    Or,

    0=x+16

    or, - 16=x

    x = - 16[impossible, as distance is never negative] so,

    x=7cm

    therefore, length = 7cm + 9 cm = 16cm and width = 7cm.

    ; )
  2. 27 November, 18:30
    0
    L = w + 9

    lw = 112

    Substitute l = w + 9 into the second equation

    (w + 9) (w) = 112

    w^2 + 9w - 112 = 0

    (w+16) (w-7) = 0

    w = - 16

    or

    w = 7

    we have to take the positive value, so w = 7

    l = w + 9

    l = 7 + 9

    l = 16

    The length is 16, and the width is 7
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