To find the value of x, we use the property of similar triangles, which states that the ratios of the lengths of corresponding sides are equal. In this case, we have two right triangles that are similar. We know the lengths of two sides from the first triangle (TR = 2 and RI = 4) and the corresponding side from the second triangle (T'R' = 7). We can set up a proportion based on these lengths: TR / T'R' = RI / R'I'. Substituting the known values gives us 2 / 7 = 4 / x. By cross-multiplying, we get 2x = 28. Dividing both sides by 2 results in x = 14. Thus, the value of x is 14.