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

Answer:

$DF = 38$

$GE = 40$

Step-by-step 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

$x = \frac{18}{3}$

$x=6$

$GE = GH + HE$

$GH= HE$

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

$y = \frac{19}{2}$

$y = 9.5$

DF is then calculated as"

$DF = DH + HF$

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

Substitute values for x and y

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

$DF = 38$