179. On two opposite banks of the river, there stands a palm tree on each. The height of one is 20 cubits, and the other is 30. The width of the river is 50 cubits. At the top of each palm tree, there sits a bird. Both birds see a fish in the river and simultaneously fly in a straight line to it, reaching the water surface at the same time at a point on the line connecting the roots of the palms. Determine the length of the paths flown by the birds and the point of their meeting.
179. Al-Karhi's Solution: Let $x$ be the distance from the meeting point to the roots of the taller palm, square it, you get $x^{2}$. Add to this 900, i.e., the square of the height of the taller palm, and set this sum equal to the square of $50-x$, i.e., $2500+x^{2}-100 x$, increased by the square of the height of the other palm, 400:

$$
x^{2}+900=2500+x^{2}-100 x+400
$$

you get $x=20$. The distance from the meeting point to the roots of the shorter palm is 30. The straight line each bird flew will be $\sqrt{1300}=10 \sqrt{13}$