## Task 31/82

In an acute triangle, one side measures 3 units, another side measures 9 units (where "units" refers to the length unit). It is known that the third side is an odd whole number of length units. Determine this number.

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The original text has been translated into English, maintaining the original formatting and line breaks.
Let $x$ be the sought (odd) number of length units. From the cosine theorem of plane trigonometry, due to the acuteness of the triangle, it immediately follows that

$$
\begin{aligned}
& x^{2}<3^{2}+9^{2} \rightarrow x^{2}<90 \rightarrow x \leq 9 \\
& 9^{2}<3^{2}+x^{2} \rightarrow 72<x^{2} \rightarrow x \geq 9
\end{aligned}
$$

Thus, $x=9$, and the triangle is isosceles.