The floor of a one-story building is 14 feet longer than it is wide (see figure). The building has 1472 square feet of floor space.

a) Write a quadratic equation for the area of the floor in terms of w.

(b) Find the length l and width w of the floor.

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  1. w (w+14) = 1472
    w^2 + 14 w - 1472 = 0

    w = [-14 +/- sqrt(196+5888) ]/2

    w = [-14 +/- 78]/2

    want positive w so
    w = 32
    then l = 32+14 = 46

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