Question

find the lengths of the segments with variable expressions. ef = 10 ad = 7 bc =

Explanation:

Step1: Identify the relationship

In a trapezoid, if $EF$ is the mid - segment, then the formula for the length of the mid - segment of a trapezoid is $EF=\frac{AD + BC}{2}$. We know that $EF = 10$ and $AD=x - 3$, $BC=2x - 7$, and since $EF = 10$, we first need to find the value of $x$. Given $EF=x$, so $x = 10$.

Step2: Calculate $AD$

Substitute $x = 10$ into the expression for $AD$. $AD=x - 3=10 - 3=7$.

Step3: Calculate $BC$

Substitute $x = 10$ into the expression for $BC$. $BC=2x - 7=2\times10 - 7=20 - 7 = 13$.

Answer:

13