Consider quadrilateral EFGH. Quadrilateral E F G H is shown. Sides F G and E H are parallel. Angles E and H are congruent. The length of E F is 4 n minus 4, the length of F G is 3 n + 3, and the length of G H is 2 n + 6. What is the length of line segment GH?

1. 5 units

2. 7 units

3. 16 units

4. 24 units

C.) 16 units

3. The length of the line segment is 16 units

Step-by-step explanation:

Considering the properties of quadrilateral, opposite sides are parallel and equal, we can find the value of n, using that n value we can find the value of segment GH.

As given in the problem, sides FG and EH are parallel and so they are equal.

So we can write, the next side EF and GH is also parallel,

EF = GH

4n-4 = 2n + 6

Grouping the terms we will get,

4n - 2n = 6 + 4

2n = 10

n = 10/2 = 5

So GH = 2 (5) + 6 = 10 + 6 = 16 units.