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Andre45 [30]
2 years ago
9

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.
Mathematics
1 answer:
miskamm [114]2 years ago
7 0

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

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