Question

Figure ABCD is a parallelogram.

What are the lengths of line segments AB and BC?

AB = 4; BC = 16

AB = 4; BC = 8
AB = 10; BC = 20
AB = 10; BC = 28

Answer 1

It is given ABCD is a parallelogram.In a parallelogram opposite sides are equal.

AB=DC and  AD=BC.

Substituting the given values in terms of x ad y we have:

3y-2=y+6                and 2x-4=x+12

Solving for x and y ,

3y-y=6+2               and      2x-x=12+4

2y=8                    and  x=16.

y=4                     and          x=16.

AB=3y-2             and        BC=x+12

AB=3(4)-2          and      BC= 16+12=28.

AB=10.

The correct answer is AB = 10; BC = 28.

Answer 2

Applying the definition of the sides of a parallelogram, AB = 10 units; BC = 30

Sides of a Parallelogram

The two pairs of opposite sides in a parallelogram are parallel to each other and are also congruent or equal in measure.

Thus:

AB = DC

• Substitute

3y - 2 = y + 6

• Combine like terms

3y - y = 2 + 6

2y = 8

y = 4

AD = BC

• Substitute

2x - 4 = x + 12

2x - x = 4 + 12

x = 18

Find AB:

AB = 3y - 2

• Plug in the value of y

AB = 3(4) - 2

AB = 10 units

Find BC:

BC = x + 12

• Plug in the value of x

BC = 18 + 12

BC = 30 units.

Therefore, applying the definition of the sides of a parallelogram, AB = 10 units; BC = 30 units.

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