Question

Determine the values of x and y. DEFG is a parallelogram. DH = x + 3 HF = 3y GH = 4x - 5 HE = 2y + 3 A) x = 2 and y = 3 B) x = 3 and y = 2 C) x = 3 and y = 6 D) x = 6 and y = 3 ?

Answer 1

`color(magenta)(x=1/2`

`color(red)(x=14/6`

Explanation:

`DH=HF` [Since diagonals bisect each other]

`x+3=3y`

`x=3y-3`

`GH=HE`

`4x-5=2y+3` [Replacing `x=3y-3`]

`4(3y-3)-5=2(3y-3)+3`

`12y-12-5=6y-6+3`

`12y-6y=-6+3+12+5`

`6y=14`

`color(red)(x=14/6`

`x=3y-3=3xx14/6-3=7/2-3=7/2-6/2`

`color(magenta)(x=1/2`

~Hope this helps! :)