Question

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. (Image attached below)thank you ! :))

Answer 1

Given:

DH = x + 1

HF = 3y

GH = 3x - 4

HE = 5y + 1.

Hence:

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

GH = HE

Substituting the given values above we get:

x + 1 = 3y (1)

3x - 4 = 5y + 1 (2)

Solving the system:

x = 3y - 1

3 (3y - 1) - 4 = 5y + 1

9y - 7 = 5y + 1

4y = 8

y = 2

x + 1 = 3 (2)

x = 5

ANSWER

the values of x and y are; 5 and 2