# Right triangle

## Main Question or Discussion Point

A large right triangle has a hypotonuse of 2000x+1125. The other sides are 2000x-1125 and x. solve for x. I have tried this with pythagoreon theorem and solving a quadratic and what not but cant get it to work out. maybe i am just making a simple mistake but i cant get it to work out.

A large right triangle has a hypotonuse of 2000x+1125. The other sides are 2000x-1125 and x. solve for x. I have tried this with pythagoreon theorem and solving a quadratic and what not but cant get it to work out. maybe i am just making a simple mistake but i cant get it to work out.
Well you should get (2000x-1125)2+x2 = (2000x+1125)2 from the pythagoreon. Then expand. What did you get from your expansion?

i get simply x^2-9000000x=0. im thinking this is wrong though because to use the quadratic formula would give you 9000000-9000000, which equals 0/2, or 0.

i get simply x^2-9000000x=0. im thinking this is wrong though because to use the quadratic formula would give you 9000000-9000000, which equals 0/2, or 0.
Well you have (2000x-1125)2+x2 = (2000x+1125)2

and (2000x-1125)2 = 4000000x2-2250000x+1265625 and (2000x+1125)2 = 4000000x2+2250000x+1265625.

How does this fall out?

Your equation above is incorrect. Further, you don't really need the quadratic equation. Anything of the form ax2 - bx = 0 = x(ax - b) so x = 0 or b/a. Also I don't think you're doing the quadratic formula correctly, you shouldn't have gotten 9000000-9000000. However 0 is a possible value for x.

Does that help?

wha happens to me was when i worked out the other side stuff got cancelled. ill have a go at it, take wha you said and let you know how it goes.

wha happens to me was when i worked out the other side stuff got cancelled. ill have a go at it, take wha you said and let you know how it goes.
Well most of it should cancel out and you should get x2 - 4500000x = 0.

Is that what you got? If so what is the answer?

this has me very confused, even though it seems like it should be easy. when i expand from the pythagorean theorem i get x^2-9000000x=0, put that in quadratic formula and i get either 9000000 or 0. which doesnt seem right and doesnt work when i apply it to the triangle. what am i doing wrong? Can someone post up an answer just so i can tr to work through it and see where i went wrong because this is driving me nuts.

Well you have (2000x-1125)2+x2 = (2000x+1125)2

and (2000x-1125)2 = 4000000x2-2250000x+1265625 and (2000x+1125)2 = 4000000x2+2250000x+1265625.

How does this fall out?

Your equation above is incorrect. Further, you don't really need the quadratic equation. Anything of the form ax2 - bx = 0 = x(ax - b) so x = 0 or b/a. Also I don't think you're doing the quadratic formula correctly, you shouldn't have gotten 9000000-9000000. However 0 is a possible value for x.

Does that help?
You're right; I did math poorly (sorry!) and forgot to double the middle term.

You have (2000x-1125)2 = 4000000x2-4500000x+1265625 and (2000x+1125)2 = 4000000x2+4500000x+1265625.

So (2000x+1125)2 = (2000x-1125)2 + x2 gives us 4000000x2+4500000x+1265625 = 4000000x2-4500000x+1265625 + x2

Like terms cancel so we get 4500000x = -4500000x + x2 or x2 - 9000000x = 0 or x(x-9000000) = 0 or x = 0, 9000000.

Make sense?

es that makes sense, that is what i got. i must have done some bad math too, because i didn't think 9000000 would work when applied to the triangle,b ut i now see it does. thanks for the help.