Question

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.
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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