Question

@OrthodoxMan The lengths of the three sides of a right triangle are consecutive integers. Find them. Idk how to do this, do you know?

Answer 1

I happen to know that a right triangle of sides 3, 4 and 5 is one that is used quite often. It just so happens that it has consecutive integers.
I have no idea how you would solve this in any other way besides knowing about the 3, 4, 5 triangle.

Answer 2

This is such a stupid question that i dont need for the rest of my life

Answer 3

hey @annie.kopliku do you know this question?

Answer 4

Yes I actually do, but it is so complicated to understand. My teacher showed me how to do this, and I had to go over it like 20 times to actually comprehend it. Hold on while I type this out.

Answer 5

Yes I know how to do this. No I don't know what took me so long to find I had a dangling notification.

Answer 6

So you know that consecutive numbers are numbers that come after each other. Such as 1,2,3,4... Now we'll be using x (because x is used for basically everything; in this case we'll let x be 0)

Do you notice how
x=0
x+1= 1
x+2= 2
x+3=3
Those are consecutive numbers.

Since the problem says we're dealing with a right triangle, it tells us that
a=x
b= x+1
c= x+2

Here comes the Pythagorean Theorem.

Answer 7

Yeah now you do the pythagorean theorem and solve for x after expanding the equation. Pretty much another polynomial question. YAY!!

Answer 8

\[x^2+(x+1)2=(x+2)^2\]

Answer 9

So interger and number are the same thing just to know? and um so i dont change any number in that equation

Answer 10

You don't substitute anything and I'm sorry it's supposed to be (x+1)^2 not times 2.

Answer 11

No. Every integer is a number but every number is not an integer.

Answer 12

^ How you put that is really confusing.

Answer 13

Lol he sounded wise tho xD

Answer 14

so am i supposed to try and get x alone with all those x's?

Answer 15

Do you know how to foil? If not, I'll help you with that. I don't understand why I can't respond immediately, like it won't let me erase my last message so I have to exit this, and wait for you to respond after everything I say.

Answer 16

Sorry, I have discrete mathematics. My professor talks like that a lot.

Answer 17

@annie.kopliku
That happens when you're not connected to this site properly. I had to refresh my browser to make it work properly.

Answer 18

Plz help me with whatever foiling is

Answer 19

What is foiling?

Answer 20

All you have to do is expand and solve for x.

Answer 21

Foiling is like getting that equation and basically "expanding it" you have to put everything on one side, if my OS wasn't malfunctioning I'd be able to show you.

Answer 22

:(

Answer 23

I guess I'll do the foiling.

Answer 24

I already got it.

Answer 25

ITS WORKING. YAYAY

Answer 26

Then showwww meeeeeeeee.

Answer 27

pweaaaaaaaaaaaaseeeeeeeeeeeee

Answer 28

\[x^2+(x+1)^2=(x+2)^2\] this turns into

\[x^2+(x+1)+(x+1)=(x+2)+(x+2)\]

Answer 29

and then what else does it turn in to?

Answer 30

Sorry, the x^2 turns into x+x

Let me redo the foiling. (This is complicated)

x + x + x + 1 + x + 1 = x +2 + x + 2

Combine all the like terms

Answer 31

Hold on let me check this again. I need to do this on paper. I'm so sorry.

Answer 32

\[x^2+2x+2=2x+4\]
\[x^2 +2x - 2x +2 - 4\]

Answer 33

I know the answer is 3,4,5 that's usually how it always is. But I'm figuring out the steps.

Answer 34

Yeah I tried that.

Answer 35

\[x^2 - 2 = 0\]

Answer 36

Well I think i see why that doesnt work...

Answer 37

OH WAIT. You did the quadratic thing wrong

Answer 38

Just know that the answer is 3 4 5 How you get there is gonna be tricky.

Answer 39

I can tell its super tricky :/

Answer 40

\[x^2 + (x+1)^2 = (x+2)^2\]
\[x^2 + x^2 + 2x +1 = x^2 + 4x + 4\]
\[2x^2 +2x + 1 = x^2 + 4x +4\]
\[2x^2 - x^2 +2x - 4x + 1 - 4 = 0\]
\[x^2 - 2x - 3 = 0\]

Answer 41

\[a^2+b^2=c^2 \] is what I started off with. Then I did,

\[(x^2) + (x+1)^2 = (x+2)^2\] I "expanded" and got

\[(x+x) + (x+x+2) = (x+x+4)\] Combining all the like terms, I got

\[4x + 2 = 2x + 4\] Simplifying it I get,

\[2x = 2 \] Dividing by 2 I get

\[x=1\]

Do you think I should substitute and get the other answers @OrthodoxMan

Answer 42

Omg how does my teacher give me this if she didnt teach it >_<

Answer 43

Alot of teachers do this later on, what grade are you in? And what math do you take?

Answer 44

Actually that isn't right. I think it would work though let me look at it again.

Answer 45

Im in 10th grade geometry

Answer 46

I seee.

Answer 47

Yeah it isn't right. You didn't deal with your quadratics right.
Remember. x*x = x^2 and x+x = 2x.

Answer 48

Go back to my answer.
\[x^2 -2x -3 = 0\]

Answer 49

I GOT THIS NOW YOU FOIL.

Answer 50

my teacher taught us this (x-3) (x+1) when you come upon those types of equations.

Answer 51

x=3

Answer 52

\[3^2+(3+1)^2=(3+2)^2\]

Answer 53

Factoring that we get:
\[x^2 +x -3x -3\]
\[(x^2 +x) + (-3x - 3)\]
\[x(x+1)-3(x+1)\]
\[(x-3)(x+1)\]

Answer 54

yeah that's what I got on my paper.

Answer 55

x = -1 is not applicable. So the answer is x = 3.

Answer 56

Teamwork.

Answer 57

HOORAY FOR TEAMWORK.

Answer 58

*high fives*

Answer 59

From here do your consecutives.

Answer 60

omg lol now i have to try and process this in my poor brain

Answer 61

*Raises hand to defend face from being high-fived*

Answer 62

If you need help processing. You know who to ask. The team of two just for you.....that was really cheesy.

Answer 63

That also rhymed, so..

Answer 64

Lol yeah you do make a good team

Answer 65

Yeah then I guess we're pretty good then. Sorry if my absence scared you guys. BATTERY DYING :O:O