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#1 2010-04-25 04:34:07

Spanky
Member
Registered: 2010-02-24
Posts: 62

Word Problem

Examining the blueprints for a rectangular room that is 17 feet longer than it is wide, an electrician determines that a wire run diagonally across this room will be 54 feet long.  What is the width of this room?

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#2 2010-04-25 05:00:30

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Word Problem

If the width of the room is x, then the length is x+17.
The diagonal of that room is √(x² + (x+17)²).
So the question in the form of an equation is x² + (x+17)² = 54².

(It'll have two answers, but you can ignore the negative one)


Why did the vector cross the road?
It wanted to be normal.

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#3 2010-04-25 05:59:30

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

Thanks mathsyperson but i still dont think i'm understanding it...

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#4 2010-04-25 06:47:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

Hi Spanky;

He used the pythagorean theorem, which says that a^2 + b^2 = c^2 where a is one side of a right triangle, b is the other side and c  is the hypotenuse - the side opposite the right angle.

Here is a link that will help:

http://www.mathsisfun.com/pythagoras.html

View Image: Clipboard.jpg

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2010-04-25 07:12:34

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

Thanks for you help guys. I just cant solve it.  I'll keep trying

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#6 2010-04-25 07:14:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

Hi Spanky;

Use the quadratic equation to solve it. Try it it and if you can't, come back and I will show you how.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2010-04-25 07:17:03

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

I tried the quadratic but it doesnt seem right to me... I think i messed up somewhere.  I got -34+/- square root 22172 / 4. I dont know what to do for there..

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#8 2010-04-25 07:19:44

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

What quadratic are you trying to solve for? Are you using these formulas?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2010-04-25 07:32:48

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

yes

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#10 2010-04-25 07:36:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

What does your quadratic look like?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#11 2010-04-25 07:46:58

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

X= -34 +/- square root (34)^2 - 4(2)(-2627) / 2(2)

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#12 2010-04-25 07:53:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

Your equation should be:


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2010-04-25 08:00:53

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

right, thats what i got, then I used the quadratic to get X= -34 +/- square root (34)^2 - 4(2)(-2627) / 2(2), but i dont know what to do from here.

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#14 2010-04-25 08:03:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

Simplify inside of the radical.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#15 2010-04-25 08:07:33

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

ok i did that and got what i posted earlier as -34+/- square root 22172 / 4.  And i dont know what to do now..

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#16 2010-04-25 08:10:08

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

Okay, remember to use parentheses, what you have is:

You can simplify that 22172 a bit more.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#17 2010-04-25 08:16:38

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

right and thats where i got stuck.  Thanks for your help, i'll keep trying.

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#18 2010-04-25 08:16:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

22172 = 4 * 5543


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#19 2010-04-25 08:26:11

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

So is the answer something like: 17/2 + 1/2 square root 5543/4 or maybe 17/2 + 1 square root 5543/2?

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#20 2010-04-25 08:32:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

There is one more step.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#21 2010-04-25 09:16:46

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

so you cant reduce the 2 and 4?

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#22 2010-04-25 09:17:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

Both the numerator and the denominator are divisible by 2.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#23 2010-04-25 15:58:29

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

Ok I got:

-17/2 + 1 square root 5543/ 2

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#24 2010-04-25 16:01:03

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Word Problem

Hi Spanky;

Just divide the numerator and the denominator by 2 to get:


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#25 2010-04-25 16:21:34

Spanky
Member
Registered: 2010-02-24
Posts: 62

Re: Word Problem

ok I see.  Thanks! So to answer the question the width would be square root 5543 - 17 / 2 ?

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