Pythagorean Theorem Triples( x-y-z) how do we know which side of the triangle is x or y, bcx we need sequence?

Question

I m trying to solve PYTHAGOREAN triples..i m confused with x-y-z. i dont know how to denote the legs of a triangle. what is x, is it horizontal or is it vertical leg in the triangle.. please give me detailed ans...

Answer 1

a and b can be either one and not the hypotenuse.
c can ONLY be the hypotenuse.
Some triples:
3-4-5 5-12-13 7-24-25 9-40-41

Here how you find them
start from 3-4-5
3*1+1 = 4, 4+1 = 5
So first set = 3-4-5
Next odd number
5*2+2 = 12, 12+1 = 13
So second set = 5-12-13
Next odd number
7*3+3 = 24, 24+1 = 25
So third set = 7-24-25
Next odd number
9*4+4 = 40, 40+1=41
So fourth set = 9-40-41

AND SO ON.....

Answer 2

c^2 - b^2 = a^2 z^2-x^2=(x+y)^2 (72ft)^2 - (x)^2 = (x+51ft)^2 (5184ft^2) - (x^2) = (x^2+2601ft^2) 5184ft^2 = x^2+2601ft^2 + x^2 2583ft^2 = x^2+x^2 2583ft^2 = 2x^2 1291.5ft^2 = x^2 x = 25.40-one ft long area = x+y long area = 25.41ft+51ft long area = seventy six.4 ft **EDIT*** I redid the question on paper, the stairs right here could be incorrect, however the respond is right. be conscious that the 1st 2 answerers are incorrect; they substituted x^2 for c^2 in c^2 - b^2 = a^2, that's erroneous, simply by fact c^2 for this reason = (x+y)^2

Answer 3

the greatest side is the
hypotnuse, other two u can
choose as horizontal
or vertical, it doesnot matter

Answer 4

it doesn't matter
a+b=b+a so
x^2+y^2=y^2+x^2