In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x − 4, and HE = 5y + 1. Find the values of x and y. The diagram is not drawn to scale.
In a parallelogram, opposite sides are equal in length. Therefore, we can set up two equations:
DH = GF ⟹ x + 1 = 3x - 4
HE = FG ⟹ 5y + 1 = 3y
Simplifying the first equation, we get:
2x = 5
x = 5/2
Simplifying the second equation, we get:
2y = -1
y = -1/2
Therefore, the values of x and y are 5/2 and -1/2, respectively.