34.0k views
3 votes
In parallelogram DEFG, segment DH is equal to 2y + 6, segment HF is equal to 4x + 1, segment HE is equal to 3x + 2, and segment GH is equal to 20. Find the values of GE and DF.

User Jaccar
by
8.0k points

1 Answer

4 votes

Final answer:

By applying the properties of a parallelogram, the value of GE and DF are determined to be 5 each, after finding y = 7 and x = 1 from the given equations.

Step-by-step explanation:

In parallelogram DEFG, we are given that segment DH is equal to 2y + 6, segment HF equals 4x + 1, segment HE equals 3x + 2, and segment GH equals 20. To find the values of GE and DF, we need to use the properties of a parallelogram that opposite sides are equal. Since DH and GF are opposite sides of a parallelogram, they must be equal. The same applies to HE and DF.

We can set up the equations as follows:

  • DH = GF ⇒ 2y + 6 = 20 ⇒ y = 7
  • HE = DF ⇒ 3x + 2 = 4x + 1

By solving the first equation, we find that y = 7. Substituting the value of y into DH, we get GH = 2(7) + 6, which simplifies to GH = 20. For the second equation, solving for x gives us x = 1. Substituting x = 1 into HE, we get HE = 3(1) + 2, which equals 5. Therefore, GE and DF both equal 5.

User Sandeepkunkunuru
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.