Chapter E, Problem 8.11EX

To determine

To find the ratio of AD to DC.

Answer to Problem 8.11EX

Option (c) $\frac{7}{9}$ is correct.

Explanation of Solution

Given information: In rt. $\Delta ABC,\overline{AB}\perp \overline{BC},\overline{BD}\perp \overline{AC}$ at point D, $BC=9$ , and $AC=12$ .

Options,

a. $\frac{9}{16}$

b. $\frac{16}{9}$

c. $\frac{7}{9}$

d. $\frac{9}{7}$

Calculation: The required solutions is obtained as,

From figure,

  $\frac{A{B}^2}{B{C}^2}=\frac{AD}{DC}=\frac{63}{81}=\frac{7}{9}$

Therefore, Option (c) $\frac{7}{9}$ is correct.