Question

In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 4x-3 and HE = 4y + 1. Find the values of x and y. The diagram is not drawn to scale.

Answer 1

Rule: The diagonals of any parallelogram bisect each other. In other words, they cut each other in half.

This means DF is cut into two equal pieces: DH and HF.
Similarly, GE is cut into two equal pieces: GH and HE.

DH = HF
x+5 = 2y
x = 2y-5

GH = HE
4x-3 = 4y+1
4(x)-3 = 4y+1
4(2y-5)-3 = 4y+1 ... x has been replaced with 2y-5
8y-20-3 = 4y+1
8y-23 = 4y+1
8y-4y = 1+23
4y = 24
y = 6

If y = 6, then x is
x = 2y-5
x = 2(6)-5
x = 12-5
x = 7

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Answers:
x = 7 and y = 6