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The length of a rectangle is three less than three times the width. The area is 90ft^2. Find the width and the length of the retangle.

  • math -

    first we represent the unknowns using variables,,
    let x = width
    let 3x-3 = length (according to the first statement)
    now we set up the equation,, since we are given the area, recall that the area of a rectangle is
    A = L*W
    where L=length and W=width.
    substituting,
    90 = (3x - 3)(x)
    90 = 3x^3 - 3x
    0 = 3x^2 - 3x - 90
    we can factor out the 3 and just cancel it (since the other side of equation is zero):
    0 = 3(x^2 - x - 30)
    0 = x^2 - x - 30
    since it's factorable,
    0 = (x+5)(x-6)
    x = -5 and x = 6
    since measurements can never be negative, we only take the positive root:
    x = 6 ft (width) ; and
    3x-3 = 15 ft (length)

    hope this helps~ :)

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