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# Triangles and Perpendiculars

ACTMAT-1LVNKK

In the figure below, $\Delta$ABC is equilateral, ${ \overline { AD } }\bot \overline{BC}$ at D, and ${ \overline { DE } }\bot \overline{AC}$ at E. If $AB = x$, then $AE = ?$

A

${\cfrac { x }{ 2 } }$

B

${\cfrac { x\sqrt { 3 } }{ 2 } }$

C

${\cfrac { x\sqrt { 3 } }{ 4 } }$

D

${\cfrac { x }{ 4 } }$

E

${\cfrac { 3x }{ 4 } }$