## Geometry: Common Core (15th Edition)

$EF = 9$
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: $EF = 9$