What is true about the lengths of opposite sides of a parallelogram? They are the same length!
The length of segment BC is 3x + 5. The length of segment AD is 5x - 13. These are equal, so
[tex] 3x+5=5x-13 \\ 5=2x-13 \\ 18=2x \\ x=9 [/tex]
Now that you know the value of x, plug that into the expression for the length of segment BC.
3x + 5 = 3(9) + 5 = 27 + 5 = 32. The length of segment BC is 32.
