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.
(picture attached below)

I have an idea on how to solve using two equations, but I'm a bit confused on how to find the values for x and y considering that each equation has both variables in it.

in summary, I'm looking for help, not the answer :)

thanks in advance! :)

Answer 1

opposite sides of a parallelogram are equal if that gives you a clue :)


Update : photo with explanation .. sorry about handwriting

Answer 2

Explanation:

It is given that In parallelogram DEFG,

DH = x + 1

HF = 3y

GH = 3x - 4

and HE = 5y + 1

Since, DH,HF, GH and HE represents the diagonals of the parallelogram and also we know that the diagonals of parallelogram bisect each other, therefore

x+1=3y (1)

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

Multiply equation (1) with 3 and then subtract equation (2) from it, we get

3x+3-3x+4=9y-5y-1

7=4y-1

y=2

Substitute the value of y=2 in equation (1), we get

x+1=3(2)

x=5

Thus,the value of x and y are 5 and 2 respectively.