Given:
In right triangle ABC, BD is the altitude drawn to hypotenuse AC.
[tex]AD=20, DC=45[/tex]
To find:
The length of BD.
Solution:
According to geometric mean theorem of triangles, if an altitude is drawn to the hypotenuse of a triangle, then the altitude is the geometric mean of the segments of the hypotenuse.
Using geometric mean theorem of triangles, we get
[tex]BD^2=AD\times DC[/tex]
[tex]x^2=20\times 45[/tex]
[tex]x^2=900[/tex]
Taking square root on both sides, we get
[tex]x=\dfrac{900}[/tex]
[tex]x=30[/tex]
Therefore, the length of BD is 30 units and the correct option is C.
