anonymous
  • anonymous
The perimeter of a rectangle is 34 cm. Given that the diagonal is of length 13 cm. Find the dimensions of the rectangle.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I should be able to help you, despite not being a tutor here. You must be in precalculus?
anonymous
  • anonymous
Yes I am currently in precalculus.
anonymous
  • anonymous
Whoa, you're back

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anonymous
  • anonymous
Sweet, okay. First off, you can split the rectangle up into four triangles, right?
anonymous
  • anonymous
Isn't it more like two? So then it becomes 2 right angle triangles where I can then use the Pythagorean Theorem?
anonymous
  • anonymous
I think it's easier to use two diagonal lines, because it makes isosceles triangles
anonymous
  • anonymous
No, I think you're right. NVM <_<;;
anonymous
  • anonymous
You want to use the Pythagoriean theorem. Also, write out the formula for perimeter. 2l + 2a = 34
anonymous
  • anonymous
a^2+l^2=13^2
anonymous
  • 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
  • anonymous
2l = 34 - 2a (I'm going to reduce this) l = 17 - a
anonymous
  • anonymous
a^2+(17-a)^2=13^2
anonymous
  • anonymous
which simplifies to a+(17-a)=13
anonymous
  • 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
  • anonymous
In other words, get l, without a square, by itself
anonymous
  • anonymous
Does that make sense?
anonymous
  • anonymous
not really :(
anonymous
  • anonymous
Don't worry ^^ I'm here to help
anonymous
  • anonymous
okay so l^2=(13-a)^2
anonymous
  • anonymous
l=(13-a)
anonymous
  • 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
  • anonymous
If you'll recall, L = 17 - a
anonymous
  • anonymous
So, (17-a)^2 = 169 - A^2
anonymous
  • anonymous
Do you remember how to foil?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Let's foil (17-a)^2
anonymous
  • anonymous
289+a^2
anonymous
  • anonymous
Nope. Remember you have to multiply both the outter and inner terms
anonymous
  • anonymous
17 * 17, then 17 * -a -a * 17, then -a * -a
anonymous
  • anonymous
Hmm, I think I need a whiteboard O_O
anonymous
  • anonymous
i get a=3.52941...
anonymous
  • anonymous
*does some math (I didn't get that far yet)
anonymous
  • anonymous
Hmm, that's not what I got. Let's keep going.
anonymous
  • anonymous
289 - 34a - a^2 = 169 - L^2
anonymous
  • anonymous
(17-a)(17-a)=-a^2-34a+289
anonymous
  • anonymous
Yup
anonymous
  • anonymous
We drop that into our equation, and then we need to clean up.
anonymous
  • anonymous
Bring all of the terms to one side.
anonymous
  • anonymous
Did I lose you? <_< (Sorry I'm a little slow, I'm tired O_O)
anonymous
  • anonymous
not really
anonymous
  • 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
  • anonymous
-a^2-34a+120=-l^2
anonymous
  • anonymous
(erm, sorry about the -l^2. That's -a^2) (I solved for l)
anonymous
  • anonymous
so -34a+120=0
anonymous
  • anonymous
Also, remember that when you square a negative, it becomes positive.
anonymous
  • anonymous
-34a=-120
anonymous
  • anonymous
a=3.5294...
anonymous
  • anonymous
So, it was a^2 - 34a +120 = -a^2 That becomes 2a^2 - 34a + 120
anonymous
  • anonymous
You forgot that when you multiply a negative by a negative, it becomes positive. (Back when you foiled)
anonymous
  • anonymous
yeah kinda tired >.>
anonymous
  • anonymous
It's fine. It's usually a stupid mistake that kills me in math.
anonymous
  • 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
  • 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
  • anonymous
k
anonymous
  • anonymous
its decomposition...
anonymous
  • anonymous
Tell what you get ^^
anonymous
  • anonymous
a=5, 12
anonymous
  • anonymous
(2a-24)(a-5)
anonymous
  • anonymous
yeah just too tired... making too many mistakes
anonymous
  • 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
  • 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
  • anonymous
Anyway, take it easy. God bless with the rest of your homework ^^
anonymous
  • anonymous
yeah you too :)
anonymous
  • anonymous
Maybe if I'm lucky, someone will help with my problem. XD

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