Task 4. Solve the system of equations $\left\{\begin{array}{l}\sqrt{x}+\sqrt{y}=10 \\ \sqrt[4]{x}+\sqrt[4]{y}=4\end{array}\right.$ and find the value of the product $x y$.
Answer: 81

Problem 5. From the vertex of the right angle $K$ of triangle $MNK$, a perpendicular $KL$ is drawn to the plane of the triangle, equal to 280. Find the distance from point $L$ to the line $MN$, given that the height of the triangle dropped from vertex $K$ is 96.

Answer: 296

Problem 6. The bank allocated a certain amount of money for loans to two companies for a period of one year. Company A received a loan amounting to $60\%$ of the allocated sum at an annual interest rate of $30\%$, and Company B received the remaining amount. After one year, when the loans were repaid, it turned out that the bank had earned a profit of $24\%$. At what interest rate was the loan given to Company B?

Answer: 15

Problem 7. In triangle $ABC$, sides $AC$ and $AB$ are equal to $6\sqrt{2}$ and $\sqrt{39}$, respectively, and the height $BH$ is equal to $\sqrt{7}$. Find the length of the median $BM$ of triangle $ABC$.

Answer: 3