Question

What are the lengths of line segments AB and BC?

Figure ABCD is a parallelogram.
A 3y - 2 B
AB = 4; BC = 16
AB = 4; BC = 8
AB = 10; BC = 20
AB = 10; BC = 28
2x - 4
y + 6
с

Answer 1

AB = 10; BC = 28

Explanation:

Just took the quiz <3

Answer 2

AB = 10 and BC = 28

Explanation:

The opposite sides of a parallelogram are congruent, thus

AB = DC, that is

3y - 2 = y + 6 ( subtract y from both sides )

2y - 2 = 6 ( add 2 to both sides )

2y = 8 ( divide both sides by 2 )

y = 4

Hence AB = 3y - 2 = (3 × 4) - 2 = 12 - 2 = 10

And

AD = BC, that is

2x - 4 = x + 12 ( subtract x from both sides )

x - 4 = 12 ( add 4 to both sides )

x = 16

Hence BC = x + 12 = 16 + 12 = 28