Question

finding lengths write similarity statements for three triangles in the diagram. then find the given length. round decimals to the nearest tenth. 19. find db. diagram of triangle with right angles at c and d, ad=16, cd=12, db=x

Explanation:

Step1: Identify geometric relationship

In a right triangle with an altitude to the hypotenuse, the length of each segment of the hypotenuse satisfies $\frac{AD}{CD} = \frac{CD}{DB}$.

Step2: Substitute known values

Plug $AD=16$, $CD=12$ into the proportion.
$\frac{16}{12} = \frac{12}{DB}$

Step3: Solve for DB

Cross-multiply and isolate $DB$.
$16 \times DB = 12^2$
$DB = \frac{144}{16}$

Answer:

$9$