Question

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

Answer 1

Step-by-step 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