Using the side formula and calling the sides a, b, c
s = (sum of all sides)/2 = perimeter/2 = 48/2 = 24
Area = square root of s(s-a)(s-b)(s-c)
c = 14
a + b = 48 - 14 = 34
==> b = 34 - a
now substitute all the new values
in to the square root 24(24-a)(24-(34-a)(24-14)
Rewrite
24(24-a)(-10+a)(24-14)
You can see that a has to be greater than 10
if we allow a to be ten we get 24 for b
==> that a is the smallest and hence the one to be adjusted to the nearest integer which is 11

Mark M.
11/25/14