Answer:
The value of x = 5 and y =2
Step-by-step explanation:
Given: In parallelogram DEFG
DH = x+1 , HF= 3y , GH =3x-4 and HE = 5y+1.
In a parallelogram DEFG as shown below in the figure,
let H be the midpoint of parallelogram where the diagonals DF and GE of a parallelogram bisect each other.
then,by definition of parallelogram;
DH = HF and
GH=HE
Since, DH =HF
Substitute the given values above we get;
x+1 = 3y
or
x-3y = -1 ......[1]
and
GH = HE
3x-4 = 5y+1
or
3x - 5y = 5 ......[2]
On solving equation [1] and [2] simultaneously we get;
y =2
Substitute the value of y=2 in [1] we have;
x -3(2) = -1 or
x-6 = -1
Add 6 to both sides of an equation:
x-6+6 = -1+6
Simplify:
x = 5
Therefore, the values of x and y is; 5 and 2
