13.052. An artificial pond has the shape of a rectangle with a difference in sides of 1 km. Two fishermen, located at one vertex of this rectangle, simultaneously set off for a point located at the opposite vertex. One fisherman swam directly along the diagonal, while the other walked along the shore. Determine the dimensions of the pond if each fisherman moved at a speed of 4 km/h and one of them arrived at the destination 30 minutes earlier than the other.

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-832.jpg?height=278&width=504&top_left_y=1517&top_left_x=746)

Fig. 13.1
## Solution.

Let $x$ km be the length of the shorter side of the pond, and $x+1$ km be the length of the second side (Fig. 13.1). Then the first fisherman swam $\sqrt{x^{2}+(x+1)^{2}}$ km, and the second walked $x+x+1$ km. According to the condition, $(x+x+1) / 4 - 0.5 = \sqrt{x^{2}+(x+1)^{2}} / 4$, from which $x=3$ km.

Answer: $3 \times 4$ km.