1. **Problem statement:** We have a right triangle with two equal sides labeled $a$ and two semicircles drawn on these sides. We want to find the sum of the diameters of both semicircles. 2. **Understanding the problem:** Each semicircle is drawn on a side of length $a$. The diameter of a semicircle is the length of the side it is drawn on. 3. **Formula and rules:** The diameter $d$ of a semicircle drawn on a side of length $a$ is simply $d = a$. 4. **Sum of diameters:** Since there are two semicircles, each with diameter $a$, the sum of the diameters is: $$\text{Sum} = a + a = 2a$$ 5. **Conclusion:** The sum of the diameters of both semicircles is $2a$. This is a straightforward problem where the sum of the diameters equals twice the length of one side $a$ of the right triangle.