Perimeter problem, need help asap!

[sweetbuck0607]

A rectangular swimming pool is to be built with a perimeter of 180 feet. The owner wants five foot wide decks along both sides and ten foot wide decks at the two ends. find the dimensions of the largest piece of property which will be needed to build the pool satisfying these conditions....i dont even know where to start

 

[tkhunny]

Are you serious? I would start by throwing this problem out with the days trash. If it REALLY says "largest", then just go with Massachusetts or somehting that big.

If it means "smallest", then it's a diferent problem.

Start by drawing the pool. It's rectangular so draw a rectangle.

Make a couple of definitions.

x = length of skinny sides of the rectangle
y = length of fat sides of the rectangle

We know the perimeter is 180 ft, so this tells us 2x + 2y = 180 ft.

Now build the deck. Let's see what you get.

 

[sweetbuck0607]

Yes, it does really say larger.
So, would my equation look like
2(x+5)^2 + 2(y+10)^2=180

 

[tkhunny]

Let's think about this a little. "largest" If the pool fits in Delaware, would it not also fit in Maine? Maine is large than Delaware. Would it not alsw fit in Russia? Russia is much larger than Maine? Would it not also fit on Jupiter? Jupiter is much larger than Russia. Do you see where I'm going with this? "largest" just makes no sense at all.

1) adding 5 and 10 is not what you want. There are borders on both sides, not just one.
2) Why is anythign squared? Is there anything in the problem statement about area?
3) You are going to have to be more clear with the definitions. As defined, is it the perimeter of the pool, itself, or the preimeter of the entire recreational location?

 

[sweetbuck0607]

The problem in my first post is the exact problem my teacher gave me, word for word.
I sorry, I probably look like an idiot, but I am horrible with story problem questions.
Not sure how to build the deck without adding 5 and 10

 

[tkhunny]

No idiots. Just pay better attention. It seems obvious, but often it isn't -- Words mean things! The word "largest" is just wrong.

When faced with a very bad problem statement, you have two paths from which to choose.

1) Punt - pan the problem statement and take your argument to the source.
2) Make some assumptions and document clearly what you are doing.

We started with:

Start by drawing the pool. It's rectangular so draw a rectangle.

Make a couple of definitions.

x = length of skinny sides of the rectangle
y = length of fat sides of the rectangle

We are now assuming that the POOL itself has perimeter of 180 ft.

We know the perimeter is 180 ft, so this tells us 2x + 2y = 180 ft.

The entire deck area, then, has a perimeter: 2(x+20) + 2(y+10) -- Notice how this is 20 and NOT 10. You must add deck to both skinny sides of the pool. It is also 10 and not 5. You must add deck to both long sides of the pool.

The pool has area x*y
The entire deck and pool has area (x+20)(y+10)
The area of the deck without the pool is (x+20)(y+10) - xy = xy + 20y + 10x + 200 - xy = 20y + 10x + 200

We're just dumping stuff we either are given or can discern from the given information.

Without another constraint, we're kind of stuck here. It may have been wiser to punt on this one.

By the way, never say that about yourself again. Who told you that?! They were wrong. You can learn.