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Required information

A $280-$lb overhead garage door consists of a uniform rectangular panel $AC,84in.$ long, supported by the cable $AE$

attached at the middle of the upper edge of the door and by two sets of frictionless rollers at A and $B.$ Each set consists of

two rollers located on either side of the door. The rollers A are free to move in horizontal channels, while the rollers $B$ are

guided by vertical channels.

Determine the distance $BD$ for which the tension in cable $AE$ is equal to $600$ lb $.$

The distance $BD$ for which the tension in cable $AE$ is equal to $600$ lb is