ANSWER
[tex]AD =2 \frac{2}{3}[/tex]
EXPLANATION
According the Altitude Theorem, the height of the triangle is equal to the geometric mean of the two segment it creates on the hypotenuse.
This implies that:
[tex] {4}^{2} =6 AD[/tex]
[tex]16 = 6 AD[/tex]
Divide both sides by 6.
[tex]AD = \frac{16}{6} [/tex]
Simplify
[tex]AD = \frac{8}{3} [/tex]
Change to mixed numbers
[tex]AD =2 \frac{2}{3} [/tex]
