If quadrilateral \(ABCD,\) pictured above, has a perimeter of 64, what is the length of line segment \(AD?\)

[Gmat_mission]

If quadrilateral \(ABCD,\) pictured above, has a perimeter of 64, what is the length of line segment \(AD?\)

(1) The length of line segment \(AD\) is equal to the length of line segment \(BC.\)

(2) Line segment \(AD\) is perpendicular to line segment \(BC.\)

[spoiler]OA=B[/spoiler]

Source: Veritas Prep