Answer
$EF = 9$
Work Step by Step
According to the trapezoid midsegment theorem, in a quadrilateral that is a trapezoid, the midsegment is parallel to the bases and is half the sum of the base lengths.
We are asked to find $EF$, which is the midsegment of this trapezoid.
Let's set up the equation to find the length of the midsegment:
$3x = \frac{1}{2}[(x + 3) + (12)]$
Evaluate parentheses first:
$3x = \frac{1}{2}(x + 15)$
Divide both sides by $\frac{1}{2}$ to get rid of the fraction. Dividing by a fraction means to multiply by its reciprocal:
$6x = x + 15$
Subtract $x$ from each side of the equation to move variables to the left side of the equation:
$5x = 15$
Divide both sides by $5$ to solve for $x$:
$x = 3$
Now we plug $3$ in for $x$:
$EF = 3(3)$
Multiply to solve:
$EF = 9$
