Question

10) Refer to - DEFG

E

4x in

F

4y in

3y +7 in

ס

113°

G

D

x+9 in

What are the lengths of EF and DG?

43 in

O 3 in

O 12 in

09 in

39 in

Answer 1

`EF = 12`

`DG = 12`

Explanation:

See attachment for complete question.

From the attachment:

`EF = 4x`

`FG = 3y + 7`

`GD = x + 9`

`DE = 4y`

Required

Solve for EF and DG

EFGD is a parallelogram. So:

`EF = DG` --- opposite sides

`FG = DE` --- opposite sides

Substitute values for EF and DG in
`EF = DG`

`4x = x + 9`

Collect Like Terms

`4x - x = 9`

`3x = 9`

Divide both sides by 3

`x = (9)/(3)`

`x = 3`

Substitute 3 for x in
`EF = 4x`

`EF = 4 * 3`

`EF = 12`

`EF = DG`

`DG = EF`

`DG = 12`