Question

Figure ABCD is a parallelogram. Parallelogram A B C D is shown. The length of A B is 3 y minus 2, the length of B C is x + 12, the length of D C is y + 6, and the length of A D is 2 x minus 4. What are the lengths of line segments AB and BC?

Answer 1

• AB = 10
• BC = 28

Explanation:

Given parallelogram ABCD with these side lengths, you want the measures of segments AB and BC.

• AB = 3y-2
• BC = x+12
• CD = y+6
• AD = 2x-4

Parallelogram

Opposite sides of a parallelogram are the same length. This lets us solve for x and y.

AB = CD

3y -2 = y +6

2y = 8 . . . . . . . . . add 2-y

y = 4 . . . . . . . . . divide by 2

AB = 3(4) -2 . . . find AB

AB = 10

BC = AD

x +12 = 2x -4

16 = x . . . . . . . . add 4-x

BC = 16 +12

BC = 28

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Answer 2

AB = 10

BC = 28

Explanation:

3y - 2

A -------------->>---------------- B

/ /

/ /

2x - 4 / / x + 12

^ ^

/ /

D --------------->>---------------- C

y + 6

Opposite sides of a parallelogram are congruent.

AB = CD

3y - 2 = y + 6

2y = 8

y = 4

BC = AD

x + 12 = 2x - 4

-x = -16

x = 16

AB = 3y - -2

AB = 3(4) - 2

AB = 10

BC = x + 12

BC = 16 + 12

BC = 28