Question

E IS THE MIDPOINT OF DF. IF DE =9X AND DF =19X -4, WHAT IF DF

Answer 1

`\begin{gathered} x=4 \\ DE=EF=9x=9\cdot4=36 \\ DF=72 \end{gathered}`

Step-by-step explanation

Step 1

Let

blue line represents DF=19x+4

black line represents DE=9x

green line represents Ef= unknow

Step 2

E is the midpoint, so

`\begin{gathered} DE+EF=DF \\ \text{replacing} \\ 9x+EF=19x-4 \\ \text{and DE=EF=9x, so} \\ 9x+9x=19x-4 \\ \end{gathered}`

Step 3

solve for x

`\begin{gathered} 9x+9x=19x-4 \\ 18x=19x-4 \\ 18x-19x=-4 \\ -x=-4 \\ x=4 \end{gathered}`

Step 4

replace the value of x to find the distances

`\begin{gathered} DE=EF=9x=9\cdot4=36 \\ DF=2\cdot DE=2\cdot36=72 \\ \end{gathered}`

I hope this helps you