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taskmasters
AC is the diagonal of parallelogram ABCD.

AE = 4x
EC = x + 3

AE = EC
4x = x + 3
4x - x = 3
3x = 3
3x/3 = 3/3
x = 1

AE + EC = AC
4x + x + 3 = AC
4(1) + 1 + 3 = AC
4 + 1 + 3 = AC
8 = AC

Choice D. 8.

Answer:

D. 8 is the length of AC.

Step-by-step explanation:

We are given,

The parallelogram ABCD with BE = ED.

So, by bisection property, we have that AE = EC.

Then, AE = EC implies,

[tex]4x=x+3\\\\4x-x=3\\\\3x=3\\\\x=1[/tex]

That is, the value of x = 1.

So, length of AE = [tex]4x=4\times 1=4[/tex]

And, length of EC = [tex]x+3=1+3=4[/tex]

Thus, the length of AC = length of AE + length of EC

That is, the length of AC = 4 + 4 = 8.

Hence, option D is correct.