## Precalculus (6th Edition)

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