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ACT® Math

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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 } } $