17. Let $A B C D$ be a square and $X$ and $Y$ be points such that the lengths of $X Y, A X$ and $A Y$ are 6,8 and 10 respectively. The area of $A B C D$ can be expressed as $\frac{m}{n}$ units where $m$ and $n$ are positive integers without common factors. Find the value of $m+n$.
17. Answer: 1041
Let the length of the side be $s$. Observe that since $6^{2}+8^{2}=10^{2}$ so $\angle A X Y=90^{\circ}$. This allows us to see that $\triangle A B X$ is similar to $\triangle X C Y$. Thus $\frac{A X}{X Y}=\frac{A B}{X C}$, i.e. $\frac{8}{6}=\frac{8}{s-B X}$. Solving this equation gives $s=4 B X$ and we can then compute that
$$
8^{2}=A B^{2}+B X^{2}=16 B X^{2}+B X^{2} .
$$

So $B X=\frac{8}{\sqrt{17}}$ and $s^{2}=16 \times \frac{64}{17}=\frac{1024}{17}$. Thus $m+n=1041$.