105. Determine the sides of a right triangle if the area and perimeter are known.
105. Let $a, b, c$ be the sides, $p$ be the perimeter, and $\Delta$ be the area.

Then $p=a+b+c ; c^{2}=a^{2}+b^{2}$ and $a b=2 \Delta$.

From the 2nd and 3rd equalities, $(a+b)^{2}=4 \Delta+c^{2},(p-c)^{2}=4 \Delta+c^{2}$, hence

$$
c=\frac{\left.p^{2}-4\right\rfloor}{2 p}
$$

Knowing $c$, we have $a+b=p-c$ and $a b=2 \Delta$. The values of $a$ and $b$ are determined as the roots of the quadratic equation.