figure abcd is a parallelogram. what are the lengths of line segments ab and bc? ab = 4; bc = 16 ab = 4; bc…

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

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

Explanation:

Step1: Use the property of parallelogram (opposite sides are equal) for sides (AD) and (BC)

In parallelogram (ABCD), (AD = BC). Given (AD=2x - 4) and (BC=x + 12), so (2x-4=x + 12). Subtract (x) from both sides: (2x-x-4=x-x + 12), which gives (x-4=12). Add (4) to both sides: (x=12 + 4=16).

Step2: Calculate the length of (BC)

Substitute (x = 16) into the expression for (BC): (BC=x + 12=16+12 = 28).

Step3: Use the property of parallelogram (opposite sides are equal) for sides (AB) and (DC)

In parallelogram (ABCD), (AB = DC). Given (AB=3y-2) and (DC=y + 6), so (3y-2=y + 6). Subtract (y) from both sides: (3y-y-2=y-y + 6), which gives (2y-2=6). Add (2) to both sides: (2y=6 + 2=8). Divide both sides by (2): (y=\frac{8}{2}=4).

Step4: Calculate the length of (AB)

Substitute (y = 4) into the expression for (AB): (AB=3y-2=3\times4-2=12 - 2=10).

Answer:

AB = 10; BC = 28 (the fourth option)