Problem with triangle task

[Szychownik]

Hello I've got problem with this task:
A rectangular triangle with a hypothetical a, b and hypotenuse c is given. Assume x if:

a= x + 2, b= 8, c= x + 6

And my question is: There's another option to solve this instead of pythagoras theorem?

[Guest]

Such a triangle can not exist .

[Guest]

Excuse me,i'm wrong.

[tex]sin^{2}[/tex][tex]\alpha[/tex]+[tex]cos^{2}[/tex][tex]\alpha[/tex]=1

([tex]\frac{a}{c})^{2}[/tex]+([tex]\frac{b}{c})^{2}[/tex]=1

([tex]\frac{x+2}{x+6})^{2}[/tex]+([tex]\frac{8}{x+6})^{2}[/tex]=1

... x=4 [tex]\Rightarrow[/tex]
a=6 , b=8 , c=10