Question

May I please get help with (5) and (6) I tried multiple times but still could not get the correct answers for each of them

Answer 1

The length of the median of a trapezoid is the average length of the bases.

(5)

`EF=(BC+AD)/(2)`

Use the equation above and the given information to find AD:

`\begin{gathered} 25=(22+AD)/(2) \\ \\ 2(25)=22+AD \\ \\ 50=22+AD \\ \\ 50-22=AD \\ \\ 28=AD \\ \\ \\ AD=28 \end{gathered}`

(6)

`LK=(BC+AD)/(2)`
`20=((8x+8)+(20-2x))/(2)`

Use the equation above to solve x:

`\begin{gathered} 20(2)=8x+8+20-2x \\ 40=6x+28 \\ 40-28=6x \\ 12=6x \\ (12)/(6)=x \\ \\ x=2 \end{gathered}`

Use the value of x to find the length of the bases:

`\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}`