# STUCK!!!!!!!!!! help me here

#### raymondtamesis

##### New member
I am unsure how to proceed to answer this problem?

A rectangular swimming pool is three times longer than it is wide. The pool is surrounded by a brick walk way 2.5 meters wide on all four sides. Find the dimensions of the pool if the area of the brick walk way is 265 meters square :?:

#### galactus

##### Super Moderator
Staff member Please pardon my drawing. It's not too symmetrical, but you get the idea. Draw a picture. It will help.

The walkway is 2.5 meters wide all around. The pool is x wide and 3x long. We know the walkways area is 265 square meters.

Let's do the right and left side of the drawing:

The walkway is 2.5 meters wide by x+5 long. See?. There are two sides like this so we have: 2(2.5)(x+5)

Now, do the top and bottom of the drawing:

It's 3x long and 2.5 wide. There are two sides like this, so we have:

2(3x)(2.5)

Put it all together:

2(3x)(2.5)+2(2.5)(x+5)=265. Solve for x.

#### Mrspi

##### Senior Member
raymondtamesis said:
I am unsure how to proceed to answer this problem?

A rectangular swimming pool is three times longer than it is wide. The pool is surrounded by a brick walk way 2.5 meters wide on all four sides. Find the dimensions of the pool if the area of the brick walk way is 265 meters square :?:
I think galactus has confused perimeter with area in his solution. So, I'll offer a response based on area (as the problem states).

let x = width of pool
then 3x = length of pool

Area = length * width
Area of pool = 3x*x
Area of pool = 3x<SUP>2</SUP>

The walkway adds 2.5 + 2.5 or 5 m to both the length and the width of the pool. For the rectangle formed by the pool and walkway together, then,
x + 5 = width
3x + 5 = length

Area of pool and walkway together = (3x + 5)(x + 5)
You'll need to multiply these binomials together.....

Would you agree with this?

Area of pool and walkway together - Area of pool = area of walkway

Substitute the expressions we have for the areas:
(3x + 5)(x + 5) - 3x<SUP>2</SUP> = 265

There's your equation....you can solve it for x, and then determine the dimensions of the pool.

I hope this helps you.

#### galactus

##### Super Moderator
Staff member
Actually, Mrspi, I tried your solution method also. It works out the same.

x=12. I just used the walkway area to solve. Thanks for the cognizance though.