We have duplicated side length a and base b. Since we have a triangle, we have the triangle inequalities:
a > 0
b > 0
2a > b
And a+b > a which doesn't add any information.
Since the perimeter p=2a+b is a whole number and b is a whole number we conclude p-b=2a is a whole number. That doesn't mean a is a whole number, it could have a fractional part of 1/2.
The perimeter constraint is
0 < 2a + b ≤ 75
The relation between a and b is
b = 2a - 4
That automatically means 2a > b so we don't have to worry about that one.
0 < 2a + 2a - 4 ≤ 75
4 < 4a ≤ 79
1 < a ≤ 79/4
1 < a ≤ 19.75
So far that gives possible a values of 1.5, 2, 2.5, ..., 19, 19.5
But we still have our other constraints, in particular
b > 0
2a - 4 > 0
2a > 4
a > 2
So our possible lengths of a are:
Answer: 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, 10.5, 11, 11.5, 12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5, 16, 16.5, 17, 17.5, 18, 18.5, 19 and 19.5
Let's check a=2.5 and a=19.5
a=2.5, b= 2a-4 = 5-4 = 1, perimeter p=2.5+2.5+1=6, seems good
a=19.5, b=2a-4=35, p=19.5+19.5+35=74, seems good
let's go outside the bounds,
a=2, b=2(2)-4=0, not a triangle, good
a=20, b=2(20)-4=36, p=20+20+36=76, over the limit, good
Seems right.