Completing the Square Word Problem

Word Problem-Mr. Kirkland-October 14, 2013

By: A. McKinnon

A rectangular swimming pool is 10 feet deep. One side of the pool is 1.5 times longer than the other. The amount of water needed to fill the swimming pool is 3840 cubic feet. Find the dimensions of the pool.

Let x be the length of the smaller side of the pool. The length of the longer side of the pool in terms of x is 1.5x ft. Write an equation for the volume of the pool in terms of x.

Simplify the left side of the equation.

Divide the 15 from both sides to isolate the x^2.

Square root both sides of the equation.

Since a length cannot be a negative the smaller side of the pool, or width, must equal 16ft.

Now you have to find the larger side of the pool, or length. The length of the longer side of the pool in terms of x is 1.5x and x=16.

Therefore the shorter side of the pool is 16ft and the longer side is 24ft.

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