Question

find the lengths of the segments with variable expressions.
ef = 11
ad = 7
bc =

Explanation:

Step1: Set up equation for similar - triangles property

Since the lines are parallel, we can use the property of similar - triangles or the mid - segment theorem. In this case, if we assume that $EF$ is the mid - segment of trapezoid $ABCD$ (by the parallel lines and the given markings), then the length of the mid - segment of a trapezoid is given by $EF=\frac{AD + BC}{2}$. We know that $EF = x$ and $AD=x - 4$ and $BC = 2x-7$. Also, since $EF = 11$, then $x = 11$.

Step2: Substitute $x$ into the expression for $BC$

Substitute $x = 11$ into the expression for $BC$. We have $BC=2x - 7$.
$BC=2\times11-7$.

Step3: Calculate the value of $BC$

$BC = 22-7$.
$BC = 15$.

Answer:

$15$