Question

GEOMETRY PLZ HELP

Answer 1

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

$\frac{AB}{BD}=\frac{BC}{AB}$

$AB^2=BC\cdot BD$

$(5)^2=BC\cdot BD$

$BC\cdot BD=25$

When triangle CAD and CBA are similar

Then,$\frac{AC}{BC}=\frac{CD}{AC}$

$AC^2=CD\cdot BC$

$(7)^2=CD\cdot BC$

$49=CD\cdot BC$

In traingle CBA, uisng pythagoras theorem

$AB^2+AC^2=BC^2$

$BC\cdot BD+BC\cdot CD=x^2$

$25+49=x^2$

$x^2=74$

Hence, option B is true.