Question

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

Answer 1

`EF=9\ units`

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=(1)/(2)[AD+BC]`

substitute the given values

`x=(1)/(2)[(x-6)+(2x-3)]`

`x=(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`