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

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

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

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

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

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

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

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

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

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

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

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

yes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

so you cant reduce the 2 and 4?

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

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

Ok I got:

-17/2 + 1 square root 5543/ 2

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

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

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

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