First we need to show that these two triangles are similar. Add up the angles 68 and 38 degrees in the first triangle, and then subtract this sum from 180 degrees. This results in 74 degrees, which matches 74 degrees in the second triangle.
Next we write and solve an equation of ratios:
6 10
----- = -------
15 x
Cross multiplying returns 6x = 150, so that x = 25.
Note that 6/15 is the ratio of the shortest sides, and 10/x is the ratio of the longest sides.
