Question

In parallelogram DEFG, DH=x+5, HF=4y, GH=2x-1, and HE=3y+4. Find the values of x and y.

a) x = 3, y = 2
b) x = 4, y = 3
c) x = 5, y = 1
d) x = 2, y = 4

Answer 1

By using the properties of a parallelogram to set up an equation from the given linear expressions, we can solve for x and y, which are x = 3 and y = 2.

In the parallelogram DEFG, we are given four linear expressions for segments DH, HF, GH, and HE. Since DEFG is a parallelogram, opposite sides are equal in length, which implies that DH + HF = GH + HE. Substituting the given expressions, we get x + 5 + 4y = 2x - 1 + 3y + 4. This equation allows us to solve for x and y.

Simplifying the equation gives us x + 4y + 5 = 2x + 3y + 3, which simplifies further to y = 2 and x = 3. Substituting these values back into the original expressions for DH, HF, GH, and HE confirms our solution is correct.