Question

What is the length of CD? In this diagram, AABC ~ AEDC.

Answer 1

Answer:

$\implies\overline {CD} = 4$

Step-by-step explanation:

$\triangle ABC \sim \triangle EDC... (given)$

$\therefore \frac{BC}{CD} = \frac{AC}{EC}..(by\: c. s. s. t)$

$\therefore \frac{20-x}{x} = \frac{20}{5}$

$\therefore \frac{20-x}{x} = \frac{4}{1}$

4x = 20- x

4x + x = 20

5x = 20

$\therefore x = {20}{5}$

$\therefore x = 4$

$\huge \purple {\boxed {\implies\overline {CD} = 4}}$