Question

The events manager at the carrington banquet hall is designing a rectangular outdoor dance

floor. to accommodate large groups, the dance floor will have an area of approximately 2,000
square feet. the manager will make the floor 15 feet longer than it is wide so that he can set
up a dj booth at one end.
to the nearest foot, what is the width of the dance floor?

Answer 1

38 feet

Explanation:

You want to know the width of a dance floor that has an area of about 2000 square feet and is 15 feet longer than wide.

Area

If w represents the width of the floor, then its length is w+15 and its area is ...

w(w+15) = 2000 . . . . . square feet

Width

Completing the square gives ...

w² +15w + 56.25 = 2056.25 . . . . . . add (15/2)² to both sides

(w +7.5)² = 2056.25 . . . . . . . . . show as a square

w +7.5 = √2056.25 . . . . . square root

w ≈ 37.846 . . . . . . . . . . subtract 7.5

The width of the dance floor is about 38 feet.

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Additional comment

The floor would be 38 ft by 53 ft, with an area of 2014 square feet.

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