Answer:
Option B is true
Step-by-step explanation:
We are given that three right triangles .Triangles ABD,CAD and CBA are similar.
When two triangles are similar then, the corresponding sidea are in equal proportion.
We have AB=5 units
AC= 7 units
BC=x
Triangles ABD is similar triangle CBA
[tex]\frac{AB}{BD}=\frac{BC}{AB}[/tex]
[tex]AB^2=BC\cdot BD[/tex]
[tex](5)^2=BC\cdot BD[/tex]
[tex]BC\cdot BD=25[/tex]
When triangle CAD and CBA are similar
Then,[tex]\frac{AC}{BC}=\frac{CD}{AC}[/tex]
[tex]AC^2=CD\cdot BC[/tex]
[tex](7)^2=CD\cdot BC[/tex]
[tex]49=CD\cdot BC[/tex]
In traingle CBA, uisng pythagoras theorem
[tex]AB^2+AC^2=BC^2[/tex]
[tex]BC\cdot BD+BC\cdot CD=x^2[/tex]
[tex]25+49=x^2[/tex]
[tex]x^2=74[/tex]
Hence, option B is true.
