In right triangle ABC, AC = 8, AB = 15, and BC = 17. Square ADEF is inscribed in the square. Find the side length of square ADEF.
Triangle(CDE) is similar to triangle(CAB).
Therefore: CD / DE = CA / AB
Since AD = x ---> DE = x.
Since CA = 8 and AD = x ---> CD = 8 - x.
Substituting: CD / DE = CA / AB ---> (8 - x) / x = 8 / 15
Cross-multiplying: 8x = 120 - 15x ---> x = 5.217