Let's have a right angle triangle. The sides have lengths equal to rational numbers. The area of the triangle is equal to 39, the length of the hypotenuse is 31.3 and the difference of the other two sides is 28.7. What are the lengths of these two sides?
This is a simple algebra exercise. Combining $b - a = 28.7$ with $a \cdot b = 2 \cdot 39$ gives $a^2 + 28.7 a - 78 = 0$. Solving this quadratic gives $a=2.5$, $b=31.2$ as the only possible answer, and you can use the hypotenuse information to double check that this is the correct solution. Not really much of a puzzle, more of a homework problem.