Question

What is the length, in units, of segment CD? A) 6 B) 8.5 C) 7 D) 9.8

Answer 1

The answer to this question is answer B

Answer 2

Answer:

D) 9.8

Step-by-step explanation:

$In \:\triangle ABC \: and \triangle CAD$

$\angle ABC \cong \angle CAD... (each\: 90\degree)$

$\angle BAC \cong \angle ACD$

(Alternate angles)

$\therefore \triangle ABC \sim \triangle CAD$

(By AA postulate)

$\therefore \frac{AB}{CA} =\frac{AC}{CD}.. (By\: csst)$

$\therefore \frac{5}{7} =\frac{7}{CD}$

$\therefore 5CD = 7\times 7$

$\therefore 5CD = 49$

$\therefore CD = \frac {49}{5}$

$\therefore CD =9.8$