Question

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

Answer 1

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

Answer 2

Yes I am currently in precalculus.

Answer 3

Whoa, you're back

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

a^2+l^2=13^2

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

Does that make sense?

Answer 17

not really :(

Answer 18

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

Answer 19

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

Answer 20

l=(13-a)

Answer 21

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

Answer 22

If you'll recall, L = 17 - a

Answer 23

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

Answer 24

Do you remember how to foil?

Answer 25

yes

Answer 26

Let's foil (17-a)^2

Answer 27

289+a^2

Answer 28

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

Answer 29

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

Answer 30

Hmm, I think I need a whiteboard O_O

Answer 31

i get a=3.52941...

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

Yup

Answer 37

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

Answer 38

Bring all of the terms to one side.

Answer 39

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

Answer 40

not really

Answer 41

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)

Answer 42

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

Answer 43

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

Answer 44

so -34a+120=0

Answer 45

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

Answer 46

-34a=-120

Answer 47

a=3.5294...

Answer 48

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

Answer 49

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

Answer 50

yeah kinda tired >.>

Answer 51

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

Answer 52

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

Answer 53

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.

Answer 54

k

Answer 55

its decomposition...

Answer 56

Tell what you get ^^

Answer 57

a=5, 12

Answer 58

(2a-24)(a-5)

Answer 59

yeah just too tired... making too many mistakes

Answer 60

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

Answer 61

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.

Answer 62

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

Answer 63

yeah you too :)

Answer 64

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