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5 March, 19:26

Solve for the given length. The length of a rectangle is 3m longer than its width. The area of the rectangle is 154^2. What is the width of the rectangle?

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  1. 5 March, 21:09
    0
    If the length of a rectangle is 3m longer than its width, then:

    L=W+3

    Is the area really 154^2? Or is it 154m^2? If yes, then:

    A=LW

    154 = (W+3) (W)

    154 = (W^2+3W)

    0=W^2+3W-154

    0 = (W-11) (W+14)

    This means either (W-11) or (W+14) is equal to zero so:

    W=11 and W=-14

    To find out let's substitute the numbers:

    154 = (11+3) (11)

    154=154

    Therefore, the width of the rectangle is 11m
  2. 5 March, 22:16
    0
    By definition the area of a rectangle is given by:

    A = (w) * (l)

    Where,

    w: width

    l: long

    We rewrite the expression based on:

    "The length of a rectangle is 3m longer than its width"

    A = (w) * (w + 3)

    We substitute the value of the area:

    154 ^ 2 = (w) * (w + 3)

    Rewrite:

    23716 = w ^ 2 + 3w

    w ^ 2 + 3w-23716 = 0

    We solve the polynomial:

    w = 152.5

    Note: the other root is negative.

    Answer:

    the width of the rectangle is:

    w = 152.5 m
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