#### Answer

$x=3\sqrt{11}$

#### Work Step by Step

The Pythagorean Theorem states that for any right triangle, $a^{2} + b^{2} =c^{2},$ where c is the length of the hypotenuse and a and b are the length of the other two sides. Plugging in the dimensions of the given triangle into the Pythagorean Theorem, we obtain:
$$15^{2} +x^{2} = 18^{2} \\ 225 + x^{2} = 324 \\ x^2 = 99 \\ x=3\sqrt{11}$$