# BC¯¯¯¯¯ is parallel to DE¯¯¯¯¯. What is AB?

Feb 4, 2017

$A B = 34$

#### Explanation:

Given $B C$ is parallel to $D E$ :

Construct line segment $B F$ parallel to $C E$,
$\implies B F = C E = 21$, as shown in the diagram.

$\implies \Delta B D F , \Delta A B C \mathmr{and} \Delta A D E$ are similar.
$\implies \frac{A B}{A C} = \frac{B D}{B F}$
$\implies \frac{A B}{42} = \frac{17}{21}$
$\implies A B = \frac{42 \times 17}{21} = 34$