Answer:
96 units
Step-by-step explanation:
If ABCD is parallelogram, then its diagonals bisect each other. This means that
Since [tex]AE=x^2-16[/tex] and [tex]EC=6x,[/tex] you get
[tex]x^2-16=6x,\\ \\x^2-6x-16=0,\\ \\D=(-6)^2-4\cdot 1\cdot (-16)=36+64=100,\\ \\x_{1,2}=\dfrac{-(-6)\pm \sqrt{100}}{2\cdot 1}=\dfrac{6\pm 10}{2}=8,\ -2.[/tex]
The distance cannot be negative, thus, [tex]x=6\ units.[/tex]
[tex]AE=8^2-16=64-16=48,\\ \\CE=6\cdot 8=48,\\ \\AC=AE+EC=48+48=96\ units.[/tex]
