Both AB and DC are 34, the opposite sides are also congruent, thus, ABCD is indeed a parallelogram.
The length of BC is 27
Since a parallelogram has opposite sides congruent, we can equate the given side lengths to solve for BC:
We know AB = 2x and DC = x + 17. Since opposite sides are equal in a parallelogram:
AB = DC:
2x = x + 17
collect the like terms
x = 17
Find BC using the value of x:
We know BC = AD = x + 10. Substitute the value of x:
BC = AD = 17 + 10
BC = 27
To further confirm, you can also check if the other pair of opposite sides (AB and DC) is congruent:
AB = 2x = 2 × 17 = 34
DC = x + 17 = 17 + 17 = 34