Answer:
[tex]EF = 12[/tex]
[tex]DG = 12[/tex]
Step-by-step explanation:
See attachment for complete question.
From the attachment:
[tex]EF = 4x[/tex]
[tex]FG = 3y + 7[/tex]
[tex]GD = x + 9[/tex]
[tex]DE = 4y[/tex]
Required
Solve for EF and DG
EFGD is a parallelogram. So:
[tex]EF = DG[/tex] --- opposite sides
[tex]FG = DE[/tex] --- opposite sides
Substitute values for EF and DG in [tex]EF = DG[/tex]
[tex]4x = x + 9[/tex]
Collect Like Terms
[tex]4x - x = 9[/tex]
[tex]3x = 9[/tex]
Divide both sides by 3
[tex]x = \frac{9}{3}[/tex]
[tex]x = 3[/tex]
Substitute 3 for x in [tex]EF = 4x[/tex]
[tex]EF = 4 * 3[/tex]
[tex]EF = 12[/tex]
[tex]EF = DG[/tex]
[tex]DG = EF[/tex]
[tex]DG = 12[/tex]
