shortest side: m - 5
longest side: m + 4
middle side: m

perimeter

let the third side’s length be m. the sides should be m-5, m+4 and m.
(m-5) + (m+4) + m ≤ 29
3m - 1 ≤ 29
m ≤ 10

remember all sides are length = distance = |AB|, the value is always > 0.
m - 5 > 0
m > 5

also, longest side < sum of 2 others
m + 4 < (m - 5) + m
m + 4 < 2m - 5
2m - m > 4 + 5
m > 9

from m > 5,
and m > 9,
and m ≤ 10
so we get 9 < m ≤ 10

because m is the third side,
answers :
4 < first side ≤ 5
13 < second side ≤ 14
9 < third side ≤ 10