Answer:
x = 16.2
Step-by-step explanation:
We can find the value of x in the figure by comparing ΔABD, ΔBCD, and ΔABC.
Let ∠BAD = α°
Then:
- for ΔABD: ∠ABD = (90-α)°
- for ΔABC: ∠ACB = (90-α)° and ∠CBD = α°
Since all 3 triangles have the same 3 angles, then the 3 triangles are similar triangles (see the 2nd attached picture). Hence:
[tex]\boxed{AD:BD:AB=BD:CD:BC=AB:BC:AC}[/tex]
[tex]AD:BD=BD:CD[/tex]
[tex]5:9=9:x[/tex]
[tex]x=9\times9\div5[/tex]
[tex]\bf x=16.2[/tex]
