The length of the median of a trapezoid is the average length of the bases.
(5)
[tex]EF=\frac{BC+AD}{2}[/tex]
Use the equation above and the given information to find AD:
[tex]\begin{gathered} 25=\frac{22+AD}{2} \\ \\ 2(25)=22+AD \\ \\ 50=22+AD \\ \\ 50-22=AD \\ \\ 28=AD \\ \\ \\ AD=28 \end{gathered}[/tex]
(6)
[tex]LK=\frac{BC+AD}{2}[/tex][tex]20=\frac{(8x+8)+(20-2x)}{2}[/tex]
Use the equation above to solve x:
[tex]\begin{gathered} 20(2)=8x+8+20-2x \\ 40=6x+28 \\ 40-28=6x \\ 12=6x \\ \frac{12}{6}=x \\ \\ x=2 \end{gathered}[/tex]
Use the value of x to find the length of the bases:
[tex]\begin{gathered} BC=8x+8 \\ BC=8(2)+8 \\ BC=16+8 \\ BC=24 \\ \\ \\ \\ AC=20-2x \\ AC=20-2(2) \\ AC=20-4 \\ AC=16 \end{gathered}[/tex]
