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 x

Answer 1

6

Explanation:

If GH equals 20 so does HE so 3x6+2=20

Answer 2

x=6

Explanation:

given that DEFG is a parallelogram and the diagonals bisect at H.

Since diagonals bisect each other in a parallelogram, we have

DH = HF and EH = HG.

GH=20 is given. i.e. 3x+2 = 20

Subtract 2

3x = 18

Divide by 3

x =6

so answer is x =6.

We can find value of y also. DH =HF=4x+1

i.e. 2y+6 = 25

y = 9.5