Answer:
[tex]BD=4\sqrt{3}\ units[/tex]
Step-by-step explanation:
we know that
[tex]AD=12\ units[/tex]
[tex]3CD=12[/tex] ----> [tex]CD=4\ units[/tex]
see the attached figure to better understand the problem
Triangles ABD and BCD are similar by AA Similarity Theorem
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{BD}{AD}=\frac{CD}{BD}[/tex]
substitute the given values
[tex]\frac{BD}{12}=\frac{4}{BD}[/tex]
[tex]BD^2=48[/tex]
[tex]BD=\sqrt{48}\ units[/tex]
simplify
[tex]BD=4\sqrt{3}\ units[/tex]
The measure of the angle BD is [tex]\rm 4\sqrt{3}[/tex] units.
Given
In triangle ABC point D is on overline AC such that AD = 3CD = 12.
Angle-Angle Similarity(AA) If two corresponding angles of the two triangles are congruent, the triangle must be similar.
When two figures are similar, then the ratio of its corresponding sides is proportional.
[tex]\rm \dfrac{BD}{AD}=\dfrac{CD}{BD}\\\\BD^2=CD \times AD\\\\BD^2=12 \times 4\\\\BD^2=48\\\\BD=4\sqrt{3}[/tex]
Hence, the measure of the angle BD is [tex]\rm 4\sqrt{3}[/tex] units.
To know more about similar triangles click the link given below.
https://brainly.com/question/8154420
