Answer: The perimeter of a parallelogram is the sum of the lengths of all four sides. In this case, the perimeter is given as 69, so we can write:
EF + FG + GH + HE = 69
We know that opposite sides of a parallelogram are equal in length, so EF = GH and FG = HE. Substituting these into the equation above, we get:
2(EF) + 2(FG) = 69
2(GH) + 2(HE) = 69
Simplifying each equation:
2(2x+15) + 2(6x+4) = 69
4x + 30 + 12x + 8 = 69
16x + 38 = 69
16x = 31
x = 31/16
Substituting x into the equation for GH, we get:
GH = 2x+15
GH = 2(31/16) + 15
GH = 31/8 + 120/8
GH = 151/8
Therefore, the value of GH is 18.875 units.
Explanation: