SOLUTION: Determine the value of x in the parallelogram when DG = 4x, EF = 5x - 6, DE = 3x + 2, GF = 2x + 8 x = [x}

Algebra ->  Parallelograms -> SOLUTION: Determine the value of x in the parallelogram when DG = 4x, EF = 5x - 6, DE = 3x + 2, GF = 2x + 8 x = [x}      Log On


   

Question 1205645: Determine the value of x in the parallelogram when
DG = 4x, EF = 5x - 6, DE = 3x + 2, GF = 2x + 8
x = [x}
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

I'll assume the order of the points (either clockwise or counterclockwise) is D, E, F, G.

Perhaps your diagram looks something like this

If so, then DE is parallel and opposite FG.
With any parallelogram, the opposite sides are congruent.
DE = FG
3x+2 = 2x+8
3x-2x = 8-2
x = 6

Also, opposite parallel sides EF and DG are congruent.
EF = DG
5x-6 = 4x
5x-4x = 6
x = 6

When x = 6, we have the following side lengths
DE = 3x+2 = 3*6+2 = 20
FG = 2x+8 = 2*6+8 = 20
This confirms the 1st equation.
EF = 5x-6 = 5*6-6 = 24
DG = 4x = 4*6 = 24
This confirms the 2nd equation.


Summary:
x = 6
DE = 20
EF = 24
FG = 20
DG = 24