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:
$2x + 1 = \frac{1}{2}[(15) + (x - 1)]$
Evaluate parentheses first:
$2x + 1 = \frac{1}{2}(x + 14)$
Divide both sides by $\frac{1}{2}$ to get rid of the fraction. Dividing by a fraction means to multiply by its reciprocal:
$2(2x + 1) = x + 14$
Distribute on the left side of the equation:
$4x + 2 = x + 14$
Subtract $x$ from each side of the equation to move variables to the left side of the equation:
$3x + 2 = 14$
Subtract $2$ from each side of the equation to move constants to the right side of the equation:
$3x = 12$
Divide both sides by $3$ to solve for $x$:
$x = 4$
Now we plug $2$ in for $x$:
$EF = 2(4) + 1$
Multiply first, according to order of operations:
$EF = 8 + 1$
Add to solve:
$EF = 9$
