Question 171389
A rectangular swimming pool has length 30 m by 20 m. There is a deck of uniform width surrounding the pool. The area of the pool is the same as the area of the deck. Write a quadratic equation to model this situation and use it to determine the width of the deck.

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The area of the pool is 30m times 20m = 600m^2.

Let x = uniform width around the pool.

Width of bigger rectangle around the pool or deck = 2x + 20.

Length of bigger rectangle around the pool or deck = 2x + 30.

The question tells us that the area of the deck = the area of the pool.

We know the area of the pool = 600m^2.

So, your equation is:

(2x + 30) (2x + 20) = 600m^2

1.Solve for x.

2.Plug your value for x in the width of the bigger rectangle given above, which is the width of the deck.

Can you take it from here?

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I received your reply.

The answer for x has to be positive.

I got two answers for x:

x = 5 and x = -30.

You did not use FOIL correctly.  That is why your answers for x were 3-digit numbers.  

Now, we totally reject x = -30 because distance is always positive.

For example. if you live 150 feet from the store, you would say:

I live 150 feet from the store.

You would not say: I live -150 feet from the store.

Now the width for the deck is: 2x + 20 and the length of the deck is

2x + 30.

To find the the right answers, replace x with 5 in BOTH expressions and you will find the right measurements for the deck of the pool.

Is this clear?