Question

DEFG is a parallelogram. Segment DH = 2y + 6, segment HF = 4x + 1, segment HE = 3x + 2 and segment GH = 20. Find the value of GE and DF.

Answer 1

`DF = 38`

`GE = 40`

Explanation:

Given

`DH = 2y + 6,`

`HF = 4x + 1,`

`HE = 3x + 2`

`GH = 20.`

See attachment for parallelogram.

Required

Find GE and DF

From the attachment:

`GH= HE`

Substitute values for GH and HE

`20 = 3x + 2`

Subtract 2 from both sides

`20-2 = 3x + 2-2`

`20-2 = 3x`

`18= 3x`

`3x = 18`

Divide both sides by 3

`x = (18)/(3)`

`x=6`

`GE = GH + HE`

`GH= HE`

So:

`GE = GH + GH`

`GE = 20 + 20`

`GE = 40`

To find DF, we find y first:

`DH = HF`

`2y + 6 = 4x + 1`

Subtract 6 from both sides

`2y +6- 6 = 4x + 1-6`

`2y = 4x + 1-6`

Substitute 6 for x

`2y = 4*6 + 1-6`

`2y = 19`

Divide both sides by 2

`y = (19)/(2)`

`y = 9.5`

DF is then calculated as"

`DF = DH + HF`

`DF = 2y+6 + 4x+1`

Substitute values for x and y

`DF = 2*9.5+6 + 4*3+1`

`DF = 38`