Ans: $-3$
By using the Pythagoras Theorem, we have
By using the Pythagoras Theorem, we have
$\begin{array}{rcl}
24^2 + (13 + r)^2 & = & (17 – 3r)^2 \\
576 + 169 + 26r + r^2 & = & 289 – 102 r + 9r^2 \\
8r^2 – 128r – 456 & = & 0 \\
r^2 – 16r – 57 & = & 0 \\
(r + 3)(r – 19) & = & 0
\end{array}$
Therefore, $r = -3$ or $r = 19$.
If $r = 19$, the length of the diagonal becomes $(17 – 3(19)) = -40\text{ cm}$. It is impossible.
Hence, $r = -3$.
