Answer:
AC = 96 units.
Step-by-step explanation:
Given ABCD is a parallelogram.
And diagonals AC and BD intersects at point E.
Note: Diagonals of a parallelogram intersects at mid-point.
E is the mid point of diagonal AC
Therefore,
AE = CE.
Plugging expression for AE and CE, we get
[tex]x^2-16 =6x.[/tex]
Subtracting 6x from both sides, we get
[tex]x^2-16-6x = 6x-6x[/tex]
[tex]x^2 -6x -16 =0[/tex]
Factoring quadratic
(x+2)(x-8) =0.
x+2 =0 => x=-2.
x-8=0 => x=8.
We can't take the length by a negative number. Therefore, x=8.
Now, plugging x= 8 in CE =6x, we get
CE = 6(8) = 48.
We need to find the length of AC.
AC would be two times of CE.
Therefore, AC = 2 × 48 = 96.
