Question

What’s the length of the segments variable expressions ??

Answer 1

Answer:

$EF=9\ units$

Step-by-step explanation:

we know that

The Trapezoid Mid-segment Theorem states that: A line connecting the midpoints of the two legs of a trapezoid is parallel to the bases, and its length is equal to half the sum of lengths of the bases

so In this problem

$EF=\frac{1}{2}[AD+BC]$

substitute the given values

$x=\frac{1}{2}[(x-6)+(2x-3)]$

$x=\frac{1}{2}[3x-9]$

$2x=(3x-9)\\3x-2x=9\\x=9$

so

$AD=x-6=9-6=3\ units$

$EF=x=9\ units$

$BC=2x-3=2(9)-3=15\ units$