Like we always do, we start with Mr. Pythagoras's theorem.
a2 + b2 = c2
Substitute in the side lengths we know.
(24)2 + x2 = (30)2
Achin' for some simplification?
576 + x2 = 900
Subtracting 576 from both sides, we get:
x2 = 324
Just square root both sides, and presto.
x = 18
For brownie points, would this triangle be considered a Pythagorean Triple? The side lengths are 18, 24, and 30, which are all whole numbers. Yes, it would be admitted into the Pythagorean Triple Club. Actually, it's probably already soaking in the Jacuzzi.