The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²

Discussion in 'Calculator Requests' started by math_celebrity, Nov 5, 2020.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²

    The frame is a rectangle. The area of a rectangle is A = lw. So were given:
    1. l = w + 1
    2. lw = 12
    Substitute equation (1) into equation (2) for l:
    (w + 1) * w = 12

    Multiply through and simplify:
    w^2 + w = 12

    We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions:
    w = 3
    w = -4

    Since width cannot be negative, we choose the positive result and have:
    w = 3

    To solve for length, we plug w = 3 into equation (1) above and get:
    l = 3 + 1
    l = 4
     

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