This is a right-angled triangle, so we can use the Pythagorean theorem to find the value of $n$.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case:
- Side $\(1: n\)$
- Side 2 : $\(2 n-1\)$
- Hypotenuse: $\(2 n+1\)$

The equation is:

$$
\((n)^2+(2 n-1)^2=(2 n+1)^2\)
$$


Now, let's expand the terms:

$$
\(n^2+\left(4 n^2-4 n+1\right)=\left(4 n^2+4 n+1\right)\)
$$


Subtract ( $\(4 n^2+1\)$ ) from both sides of the equation:

$$
\(n^2-4 n=4 n\)
$$


Add $4 n$ to both sides:

$$
\(n^2=8 n\)
$$


Divide both sides by $n$ (we know $\(n \neq 0\)$ because it's a side length of a triangle):



$$
\(n=8\)
$$


Since the question asks for the length of the hypotenuse, we need to substitute the value of $n$ back into the expression for the hypotenuse.

$$
\(\begin{aligned}
& \text { Hypotenuse }=2 n+1 \\
& \text { Hypotenuse }=2(8)+1 \\
& \text { Hypotenuse }=16+1 \\
& \text { Hypotenuse }=17
\end{aligned}\)
$$


Therefore, the length of the hypotenuse is 17.
This corresponds to option (B).