Question

Find the length of segment with a variable expressions 

Answer 1

Explanation:

Joe, do you recall this formula ? mid-segment =
`(1)/(2)`(base1 + base2) ?

where AD = base1

and BC = base2

and mid-segment is EF

recall that this formula works, as long as EF is at the mid-point between the two top and bottom bases only.

The trapezoid is telling us , with the same length lines, that this is the case.

Then

EF =
`(1)/(2)`( x-3 + 2x -10 )

see how I got that?

EF =
`(1)/(2)`( 3x -13 )

EF =
`(3)/(2)`X -
`(13)/(2)`

also remember that EF = x

x =
`(3)/(2)`X -
`(13)/(2)`

x +
`(13)/(2)` =
`(3)/(2)`X -
`(13)/(2)` +
`(13)/(2)`

x +
`(13)/(2)` =
`(3)/(2)`X

x - x +
`(13)/(2)` =
`(3)/(2)`X - x

`(13)/(2)` =
`(1)/(2)`X

`(2)/(1)` *
`(13)/(2)` =
`(2)/(1)` *
`(1)/(2)`X

13 = x

EF = 13 :)