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

in parallelograms the diagonals bisect each other. this means that one diagonal cuts the other diagonal at its mid point.
GE cuts DF at H, then DH = HF
DH = x + 3
HF = 3y
Since DH = HF
x + 3 = 3y
3y - x = 3---->1)
GH = HE
4x - 5 = 2y + 3
4x - 2y = 3 + 5
4x - 2y = 8 ---> 2)
we have a set of simultaneous equations where we have to solve for x and y
3y - x = 3---->1)
4x - 2y = 8 ---> 2)
multiply 1st equation by 4
12y - 4x = 12 ---3)
add 2nd and 3rd equation
10 y = 20
y = 2
substitute y = 2 in 1st equation
3*2 - x = 3
6 - x = 3
x = 3 and y = 2
therefore correct response is B)