Answer:
D is the correct option.
Step-by-step explanation:
Let us apply the Pythagorean theorem in the right angle triangles.
In right angle triangle ABC
[tex]24^2=AB^2+AC^2......(1)[/tex]
Now, in right angle triangle ABD,
[tex]AB^2=AD^2+4^2\\AB^2=AD^2+16.......(2)[/tex]
Now, in right angle triangle ADC,
[tex]AC^2=AD^2+20^2\\\\AC^2=AD^2+400[/tex]
From equation (1) and (2)
[tex]24^2-AB^2=AD^2+400\\\\24^2-(AD^2+16)=AD^2+400\\\\576-AD^2-16=AD^2+400\\\\2AD^2=160\\\\AD^2=80\\\\AD=4\sqrt{5}[/tex]
