4.2. The sum of the lengths of the legs of a right triangle is $8 \mathrm{~cm}$. Can the length of the hypotenuse be 5 cm?
4.2. Let $a$ and $b$ be the legs, and $c$ be the hypotenuse of a right triangle. According to the condition, $a+b=8$, i.e., $b=8-a$. Suppose $c=5$; then we get the equation $a^{2}+(8-a)^{2}=5^{2}$, or $a^{2}+$ $+64-16a+a^{2}-25=0$, or $2a^{2}-16a+39=0$. But $\frac{D}{4}=64-2 \cdot 39<$ $<0$ and, therefore, this equation has no roots. Thus, the length of the hypotenuse cannot be $5 \text{cm}$.

Answer: no, it cannot.