Question

"Find the length of AC for which ABCD is a parallelogram.

A. 4
B. 6
C. 7
D. 8"

Answer 1

D. 8 is the length of AC.

Explanation:

We are given,

The parallelogram ABCD with BE = ED.

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

Then, AE = EC implies,

`4x=x+3\\\\4x-x=3\\\\3x=3\\\\x=1`

That is, the value of x = 1.

So, length of AE =
`4x=4* 1=4`

And, length of EC =
`x+3=1+3=4`

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.

Answer 2

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.