Question

In parallelogram DEFG, Dh=x+3, HF= 3y, GH=3x-3, and HE=5y+4. Find the values of x and y?

Answer 1

I'm assuming that H is the point at which the diagonals meet. If so you can solve it if you note that in a parallelogram each diagonal bisects the other - that is it divides the other diagonal into two equal pieces.

You are given the size of each of those pieces in terms of x and y and since you know that each opposite piece is equal you can write an equation relating them.

For example the piece from D to H is of length x+3 and the piece from H to F is 3y. I am assuming that F is opposite D, so you can write that x+3 = 3y.

If you do the same for the other diagonal you then just need to move the x and y terms to the right of both equations, and the constant terms to the left and solve as simultaneous equations.

Sorry this is a long explanation, a diagram would be much easier to understand but my drawing skills with a mouse are poor. Let me know if you get stuck on any stage.

Answer 2

yes thank you so much