Answer:
AC=96 units.
Explanation:
We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.
, and CE=6x .
Note: The diagonals of a parallelogram intersects at mid-point.
Therefore, AE = EC.
Plugging expressions for AE and EC, we get
![x^2-16=6x.](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ozc2gschgri6kgqgiwef2d4bnncgguc86s.png)
Subtracting 6x from both sides, we get
![x^2-16-6x=6x-6x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nby58gl712b4u7aa3zc72nmrgip7i2721g.png)
![x^2-6x-16=0](https://img.qammunity.org/2020/formulas/mathematics/middle-school/s6ivp5c2bkxuudu9n5jkpaqy55nf0gqi2h.png)
Factoriong quadratic by product sum rule.
We need to find the factors of -16 that add upto -6.
-16 has factors -8 and +2 that add upto -6.
Therefore, factor of
quadratic is (x-8)(x+2)=0
Setting each factor equal to 0 and solve for x.
x-8=0 => x=8
x+2=0 => x=-2.
We can't take x=-2 as it's a negative number.
Therefore, plugging x=8 in EC =6x, we get
EC = 6(8) = 48.
AC = AE + EC = 48+48 =96 units.