Given:
AB = x + 3
DC = 2x - 6
A parallelogram is a quadilateral that has two equal parallel sides.
Thus:
AB = DC
BC = AD
To find the length of the side AB, equate AB and CD since they are equal.
We have:
AB = DC
x + 3 = 2x - 6
Solve for x:
x + 3 = 2x - 6
Subtract 3 from both sides:
x + 3 - 3 = 2x - 6 - 3
x = 2x - 9
Subtract 2x from both sides:
x - 2x = 2x - 2x - 9
x - 2x = -9
-x = -9
Divide both sides by -1:
[tex]\begin{gathered} \frac{-x}{-1}=\frac{-9}{-1} \\ \\ x=9 \end{gathered}[/tex]
To find AB, substitute 9 for x in (x + 3).
AB = x + 3
AB = 9 + 3 = 12
Therefore, the length of side AB is = 12
ANSWER:
12
