Question

Ef is the median of trapezoid abcd (please explain the answer im so confused lol)

Answer 1

Explanation:

Okay, so...

The Median of a trapezoid is directly in the middle. For some weird mathimatical reason you won't ever need to know unless it's on an exam or you become a math major, its midsegment is the average of the top length and the bottom length.

In other words,

EF = ( BC + AD ) / 2

So for part 1, we can use that equation to find x.

`EF = ( BC + AD ) / 2`

• Insert known equations.

`4x-18=[(x+12)+(3x-4)]/2`

• Simplify within parentheses.

`4x-18=[x+12+3x-4]/2`

`4x-18=[x+3x+12-4]/2`

• Add.

`4x-18=[4x+8]/2`

• Divide.

`4x-18=2x+4`

• Simplify.

`(4x-2x) +(-18+18)=(2x-2x)+(4+18)`

`2x=22`

• Divide both sides by 2.

`x=11`

Part 2 is a lot easier now. All we have to do is plug in 11 for x.

`BC =x+12`

`BC = 11+12`

`BC = 23`

-

`AD = 4x-18`

`AD = 4(11)-18`

`AD = 44-18`

`AD = 26`

-

`EF = 3x-4`

`EF = 3(11)-4`

`EF = 33-4`

`EF = 29`

Answer:

Part I: x = 11

Part II:

• BC = 23
• AD = 26
• EF = 29