Answer:
28 units
Step-by-step explanation:
ABCD is a rectangle. AC and BD are diagonals intersecting at point E.
Diagonals of a rectangle bisect each other.
[tex] \therefore BE = ED[/tex]
[tex] \therefore 6x + 2 = 4x + 6[/tex]
[tex] \therefore 6x - 4x= 6-2[/tex]
[tex] \therefore 2x= 4[/tex]
[tex] \therefore x= \frac{4}{2} [/tex]
[tex] \therefore x= 2 [/tex]
[tex] \therefore 6x + 2= 6*2+2= 12+2= 14 [/tex]
[tex] \therefore BE= 14\: units [/tex]
[tex] \because BD = 2BE[/tex]
[tex] \therefore BD = 2(14)= 28\: units [/tex]
[tex] \because AC = BD[/tex] (diagonals of a are equal in measure)
[tex] \therefore AC = 28\: units [/tex]
