What is the value of x in the diagram below?

1. Identify similar triangles: The diagram shows two right-angled triangles. Both triangles share an acute angle (marked with an arc). Since they are both right-angled and share another acute angle, they are similar by the Angle-Angle (AA) similarity criterion.

1. Set up the proportion: For similar triangles, the ratio of corresponding sides is equal. Let the first triangle have sides 12 and 54, and the second triangle have sides 2 and x. The side of length 12 in the first triangle corresponds to the side of length 2 in the second triangle (both are opposite the shared acute angle). The side of length 54 in the first triangle corresponds to the side of length x in the second triangle (both are the hypotenuses).

Therefore, we can set up the proportion:
$$\frac{12}{2} = \frac{54}{x}$$

3. Solve for x: To solve for x, we can cross-multiply:
$$12 \times x = 2 \times 54$$
$$12x = 108$$

Now, divide both sides by 12:
$$x = \frac{108}{12}$$
$$x = 9$$