Question

The hypotenuse of a right triangle is 2 cm longer than one leg and 4 cm longer than the other leg.
Let x represent the length of the hypotenuse. Use the Pythagorean Theorem to write an equation that can be solved for x.

Answer 1

Ok so first things first what is the Pythagorean theorem? Write it out please

Answer 2

That's all there really says, I dont know how to get it @jtug6

Answer 3

Okay, well, for reference remember that the Pythagorean theorem is written as:

c^2 = a^2 + b^2

(Note that this can only be used for right triangles)

Where the c variable is the hypotenuse and the a/b variables are the legs

Answer 4

Ok so like x=c+2...? something like that?

Answer 5

Sorry I am not great at this

Answer 6

Ok you have the right mindset but let's try to look at what we're given first and compare it to the pythag theorem

So first thing we have is that the hypotenuse (c) is x so we can replace c with x. Now, we have two legs. It says that the hypotenuse is two cm greater than one leg and then four cm greater than another.

Answer 7

Now if the hypotenuse is two cm greater then one leg, we can use A or B either works. So greater means that we should be subtracting 2 and 4 from the hypotenuse in order to solve for x. So now we have one leg that equals x - 2 and one that equals x - 4

Answer 8

Because if you think about it if it were instead x+2 and x+4 and you re-think about it, thats basically saying leg A/B are 2 and 4 cm greater than the hypotenuse, not the hypotenuse is greater than 2cm and 4cm.

Answer 9

Oh ok

Answer 10

Sorry if its a tad confusing i'll write it out so it makes more sense:

x - 2, x - 4 means leg is 2 and 4 smaller then hypotenuse
x + 2, x + 4 means leg is 2 and 4 cm greater than the hypotenuse

The question said its hypotenuse was longer then the legs so we'd have to choose the top one

Answer 11

Yeah i understand

Answer 12

Ok neat. So now we have leg A/B which can be either or but we'll just say A = (x-2) and B = (x- 4).

Now we have:
c = x
a = x - 2
b = x - 4

Plug those back into c^2 = a^2 + b^2 and what do you get?

Answer 13

Sorry I'm not sure.

Answer 14

Am really stressed out right now cause I was put in a class 2 levels higher than I was supposed to go to..

Answer 15

I kinda understand the concept however

Answer 16

Ah. I can understand that. Ok well everything is being squared right? So if we have what c/a/b equal we can just square everything so that it looks like this:

x^2 = (x-2)^2 + (x-4)^2

Answer 17

Okay

Answer 18

Thank you :)

Answer 19

mhm. youre just rewriting in terms of a/b/c then plugging back in. what class are you in then? algebra 1 or 2?

Answer 20

Im taking geometry b. I didnt take geometry a nor did i take the algebra so its confusing

Answer 21

Yeah, not sure what geometry a/b is though. I'm guessing thats like part 1 and part 2? Perhaps consult with your counselor to get things straightened out? I can help you out whenever you need it. Geometry is merely postulates and very basic understanding of properties of triangles.