The perimeter of the triangle is 5a. One of the sides is equal to a + b, the second is less than Her by 2a.

The perimeter of the triangle is 5a. One of the sides is equal to a + b, the second is less than Her by 2a. Determine the third side of the triangle.

If one of the sides of the triangle is equal to a + b, and the second is less than it by 2 * a, then the second side is equal to a + b – 2 * a = b – a.
Suppose the third side of the triangle is x. If the sides of the triangle a, b and c are known, then the perimeter P of this triangle will be equal to P = a + b + c. According to the terms of the assignment, the perimeter of the triangle is 5 * a. Therefore, for our triangle, based on the conditions of the task, it can be argued that (a + b) + (b – a) + x = 5 * a or 2 * b + x = 5 * a.
Let’s solve the resulting equation for the unknown x. We have: x = 5 * a – 2 * b.
So the third side of the triangle is 5 * a – 2 * b.
As a note, it should be noted that there are certain conditions for the existence of triangles, for example, the side of a triangle is greater than zero. If, for some reason, at least one condition for the existence of triangles is violated, then the problem, and therefore the answer, will not make sense.
Answer: The third party is 5 * a – 2 * b.