Question 957249
use Pythagorean theorem to find the length of hypotenuse {{{c}}} of right angle triangle:

{{{c^2=a^2+b^2}}}

given: two sides 

{{{a= 2x(x+1)}}} and {{{b=2x+1}}}
{{{a= 2x^2+2x}}}

{{{c^2=(2x^2+2x)^2+(2x+1)^2}}}

{{{c^2=4x^4+8x^3+4x^2+4x^2+4x+1}}}

{{{c^2=4x^4+8x^3+8x^2+4x+1}}}

{{{c^2=(2x^2+2x+1)^2}}}

{{{c=sqrt((2x^2+2x+1)^2)}}}

{{{c=2x^2+2x+1}}}

so, the length of hypotenuse is {{{highlight(2x^2+2x+1)}}}