# Math Help - Rectangular Swimming Pool

1. ## Rectangular Swimming Pool

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.

2. <----20+2x---->
_____________
|...................|...^
|.....__20__... |....|
|..x.|........ |...|...|
|....|.........|30|...30+2x
|....|_____ |...|....|
|...................|....|
|____________|... v

Pool area = $600m^2$

Deck area = $(30 + 2x)(20 + 2x) = 600$

$4x^2 +100x - 600 = 0$

$x^2 +25x - 150 = 0$

$(x + 30)(x - 5) = 0$

$x = 5$ (width can't be -30)

width of deck = 20 + 2x = 20 + 10 = 30m.

3. ## but.....

Originally Posted by nzmathman
<----20+2x---->
_____________
|...................|...^
|.....__20__... |....|
|..x.|........ |...|...|
|....|.........|30|...30+2x
|....|_____ |...|....|
|...................|....|
|____________|... v

Pool area = $600m^2$

Deck area = $(30 + 2x)(20 + 2x) = 600$

$4x^2 +100x - 600 = 0$

$x^2 +25x - 150 = 0$

$(x + 30)(x - 5) = 0$

$x = 5$ (width can't be -30)

width of deck = 20 + 2x = 20 + 10 = 30m.
I thank you for the reply.

However, I am slightly lost using the FOIL method in this case.

We have:

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

On the left side, I got this:

4x^2 + 100x + 600 = 600

I then subtracted 600 from both sides and got this:

4x^2 + 100x = 0

How did you get -600 on the left side of the equation?

4. Sorry about that. It should say:

$(30 + 2x)(20 + 2x) = 1200\,\,$ (because looking at the diagram $(30 + 2x)(20 + 2x)$ is the whole combined area of the deck and pool).

$(30 + 2x)(20 + 2x) = 1200$

$4x^2 + 100x + 600 = 1200$

$4x^2 + 100x - 600 = 0$

5. ## ok.............

Originally Posted by nzmathman
Sorry about that. It should say:

$(30 + 2x)(20 + 2x) = 1200\,\,$ (because looking at the diagram $(30 + 2x)(20 + 2x)$ is the whole combined area of the deck and pool).

$(30 + 2x)(20 + 2x) = 1200$

$4x^2 + 100x + 600 = 1200$

$4x^2 + 100x - 600 = 0$
Now it makes sense.