Answer
$x = 6$
Work Step by Step
A line segment joins the midpoint of two of a triangle's sides. According to the triangle midsegment theorem, if a line segment joins two sides of a triangle at their midpoints, then that line segment is parallel to the third side of that triangle and is half as long as that third side.
Knowing this information, we can deduce that the third side is parallel to the midsegment, the line segment that joins the midpoints of the other two sides of the triangle. It also means that this third side is two times the length of the midsegment. Let's set up an equation to find the value of $x$ using this information:
$4x = 2(12)$
Multiply to simplify:
$4x = 24$
Divide by $4$ on each side to solve for $x$:
$x = 6$
