The three sides of a right angle triangle are given as $\(n, 2 n-1 \& 2 n+1\)$

As n is a positive integer, the greatest of the three sides i.e. hypotenuse must be $\(2 \mathrm{n}+1\)$

Now, applying Pythagoras theorem i.e. Hypotenuse $\({ }^2=\)$ Perpendicular $\(^2+\)$ Base $^2$ in the triangle we get $\((2 n+1)^2=(2 n-1)^2+(n)^2\)$ which when simplified gives $\(n^2-8 n=0 \Rightarrow n=0$ or $n=8\)$

The value of $n$ cannot be zero, so it has to be 8 .
Thus, the length of the hypotenuse $\(=2 n+1=2 \times 8+1=17\)$.
Hence the answer is (D).