The perimeter of a rectangle is 34 cm. Given that the diagonal is of length 13 cm. Find the dimensions of the rectangle.

- anonymous

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- anonymous

I should be able to help you, despite not being a tutor here. You must be in precalculus?

- anonymous

Yes I am currently in precalculus.

- anonymous

Whoa, you're back

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## More answers

- anonymous

Sweet, okay. First off, you can split the rectangle up into four triangles, right?

- anonymous

Isn't it more like two? So then it becomes 2 right angle triangles where I can then use the Pythagorean Theorem?

- anonymous

I think it's easier to use two diagonal lines, because it makes isosceles triangles

- anonymous

No, I think you're right. NVM <_<;;

- anonymous

You want to use the Pythagoriean theorem.
Also, write out the formula for perimeter.
2l + 2a = 34

- anonymous

a^2+l^2=13^2

- anonymous

The trick is to use a substituion.
pick either l or a , and solve for it.
In this case, I'll pick L

- anonymous

2l = 34 - 2a (I'm going to reduce this)
l = 17 - a

- anonymous

a^2+(17-a)^2=13^2

- anonymous

which simplifies to a+(17-a)=13

- anonymous

Yup. I don't think that's the proper way to substitute in this case.
Solve for l on a^2+l^2 = 13^2

- anonymous

In other words, get l, without a square, by itself

- anonymous

Does that make sense?

- anonymous

not really :(

- anonymous

Don't worry ^^ I'm here to help

- anonymous

okay so l^2=(13-a)^2

- anonymous

l=(13-a)

- anonymous

Okay. First off, let's get L^2 by itself
A^2 + L^2 = 13^2
This changes to L^2 = 169 - A^2

- anonymous

If you'll recall, L = 17 - a

- anonymous

So, (17-a)^2 = 169 - A^2

- anonymous

Do you remember how to foil?

- anonymous

yes

- anonymous

Let's foil (17-a)^2

- anonymous

289+a^2

- anonymous

Nope. Remember you have to multiply both the outter and inner terms

- anonymous

17 * 17, then 17 * -a
-a * 17, then -a * -a

- anonymous

Hmm, I think I need a whiteboard O_O

- anonymous

i get a=3.52941...

- anonymous

*does some math (I didn't get that far yet)

- anonymous

Hmm, that's not what I got. Let's keep going.

- anonymous

289 - 34a - a^2 = 169 - L^2

- anonymous

(17-a)(17-a)=-a^2-34a+289

- anonymous

Yup

- anonymous

We drop that into our equation, and then we need to clean up.

- anonymous

Bring all of the terms to one side.

- anonymous

Did I lose you? <_< (Sorry I'm a little slow, I'm tired O_O)

- anonymous

not really

- anonymous

Okay. (I'm trying not to do all the work for you.) Please bring all of the terms to one side of the equation, and post them. (We're close to being done)

- anonymous

-a^2-34a+120=-l^2

- anonymous

(erm, sorry about the -l^2. That's -a^2) (I solved for l)

- anonymous

so -34a+120=0

- anonymous

Also, remember that when you square a negative, it becomes positive.

- anonymous

-34a=-120

- anonymous

a=3.5294...

- anonymous

So, it was a^2 - 34a +120 = -a^2
That becomes
2a^2 - 34a + 120

- anonymous

You forgot that when you multiply a negative by a negative, it becomes positive. (Back when you foiled)

- anonymous

yeah kinda tired >.>

- anonymous

It's fine. It's usually a stupid mistake that kills me in math.

- anonymous

The next step is to reduce. Always reduce whenever you can, because it makes it math easier. (I don't know about you, but I'm lazy when it comes to math:P)
So, 2a^2 - 34a + 120 becomes
a^2 - 17a + 120

- anonymous

All you need to do is factor, and you'll get your answer. s. It's plural. You can use the perimeter formula thingie to double check your answer.

- anonymous

k

- anonymous

its decomposition...

- anonymous

Tell what you get ^^

- anonymous

a=5, 12

- anonymous

(2a-24)(a-5)

- anonymous

yeah just too tired... making too many mistakes

- anonymous

It's fine! You're pro now! Those answers are correct. ^^ 144 + 25 = 169
If you want to impress (cough) your math teacher, you can write the answer as
if a = 5, then l = 12, or if a = 12, then l = 5

- anonymous

The reason either answer works, is because we don't know which way the rectangle is orientated.
Oh, and on a funny note, I tried solving the problem with trig. (I'm in Trig right now. That's the math class after precalc) It completely... Did not work. XD Yeesh, I'm tired too. I made some mistakes.

- anonymous

Anyway, take it easy. God bless with the rest of your homework ^^

- anonymous

yeah you too :)

- anonymous

Maybe if I'm lucky, someone will help with my problem. XD

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