#### Answer

$x^{2}+(2x-2)^{2}$ $=$ $(x+4)^{2}$

#### Work Step by Step

In the given triangle, $(x+4)$ is the hypotenuse whereas $x$ and $(2x-2)$ form the arms of the triangle.
According to the Pythagoras theorem,
$ {a^{2}+b^{2}}$ $=$ $c^{2}$
Where a and b are arms of triangle and c is the hypotenuse.
Substituting the values in the above formula we get,
$x^{2}+(2x-2)^{2}$ $=$ $(x+4)^{2}$
Hence, the answer is option D.