Answer :

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]

View image karmenchong
View image karmenchong