Answer
The side is 17 inches long, and the altitude to that side is 6 in.
Work Step by Step
We know the following equation:
$A = .5bh$
Since $ b = 3h -1$, we obtain:
$ 51 = .5(3h-1)(h) \\ 102 = 3h^2 -h \\ 3h^2 -h -102 = 0 \\ (h-6)(3h+17)$
Ignoring negative solutions, we find:
$h = 6 \\ b = 3h -1 = 3(6) -1 =17$
