Answer:
56
Step-by-step explanation:
Let CD = x and BD = y
In triangle ABC [tex]AB^{2} = 16^{2} + 30^{2}[/tex] by the Pythagorean theorem.
So [tex]AB^{2} = 256 + 900 = 1156\\\\AB = \sqrt{1156} = 34[/tex]
Now in triangle ABD
[tex]AB^{2} + BD^{2} = AD^{2} \\\\34^{2} + y^{2} = (x + 16)^{2}[/tex] by the Pythagorean theorem
[tex]1156 + y^{2} = x^{2} + 32x + 256[/tex]
[tex]y^{2} = x^{2} + 32x - 900[/tex]
and in triangle ACD [tex]30^{2} + x^{2} = y^{2}[/tex] by the Pythagorean theorem
Now
[tex]y^{2} = x^{2} + 32x - 900 = 900 + x^{2} \\\\32x = 1800\\\\x = 56.25[/tex]
