The lengths of line segments AB and BC are AB = 10; BC = 28
Parallelograms are shapes with parallel and equal opposite sides
The given parameters are:
AB = 3y - 2
BC = x + 12
DC = y + 6
AD = 2x - 4
The above means that:
AB = DC
BC = AD
So, we have:
AB = DC
3y -2 = y + 6
Collect like terms
3y - y = 2 + 6
2y = 8
Divide by 2
y = 4
Also, we have:
BC = AD
x + 12 = 2x - 4
Collect like terms
2x - x = 4 + 12
x = 16
The lengths AB and BC are given as:
AB = 3y - 2
BC = x + 12
So, we have:
AB = 3*4 - 2
AB = 10
BC = x + 12
BC =16 + 12
BC = 28
Hence, the lengths of line segments AB and BC are AB = 10; BC = 28
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