Question

example 7: in the diagram below, figure abcd is a parallelogram. what is the length, in units, of ac?

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $AE = EC$ and $DE = EB$. First solve for $y$ using $AE = EC$:
$3y + 2 = 2y$

Step2: Solve for y

Subtract $2y$ from both sides:
$3y - 2y + 2 = 0$
$y = -2$

Step3: Calculate length of AE

Substitute $y=-2$ into $AE = 3y+2$:
$AE = 3(-2) + 2 = -6 + 2 = -4$
(Note: Length is positive, so $|AE|=4$, $EC=4$)

Step4: Calculate total length AC

$AC = AE + EC$
$AC = 4 + 4 = 8$

Answer:

8