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# A rectangular swimming pool is 60 ft wide and 80 ft long. A nonskid surface of uniform width is to be installed around the pool. If there is 576 ft^2 of the

see here for end of question: nonskid material, how wide can the strip of the nonskid surface be?

Hi Susana,

Let's start with the area of the pool itself, which we know is 60 x 80 = 4800 square feet. If we let the width of the nonskid surface be x, then the width of the pool + nonskid surface is 60 + 2x, and the length of the pool + nonskid surface is 80 + x. So, the total area of the pool including the nonskid surface is length x width, or (60 + 2x)((80+ 2x). The total area of the pool + nonskid surface minus the area of just the pool is the area of just the nonskid surface, or mathematically:

(60 + 2x)(80 + 2x) - 4800 = 576

After expanding, we have:

4800 + 160x + 120x + 4x^2 = 5376

Combining like terms gives:

4x^2 + 280x - 576 = 0

Dividing all terms by 4 gives:

x^2 + 70x - 144 = 0

This quadratic can be solved by factoring or with the quadratic formula. Factoring gives:

(x+72)(x-2) = 0

The solutions are then x = -72 and x = 2. We know the nonskid material cannot be -72 feet wide, so the only solution that makes sense is x = 2.

So the width is 2 feet.