Question

Figure ABCD is a parallelogram What are the lengths of line segments AB and BC?

Answer 1

Question is Incomplete,Complete question is given below;

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:

AB = 10 ;BC =28.

Step-by-step explanation:

The Diagram is missing in the question we have attached the diagram for your reference.

Given:

AB = $3y -2$

DC = $y+6$

BC = $x+12$

AD = $2x-4$

We need to find the lengths of AB and BC.

Solution:

Since given that Figure ABCD is a parallelogram.

"The opposite side of parallelogram are equal."

Hence we can say that;

AB = DC

Substituting the value we get;

$3y-2=y+6$

Combining the like terms we get;

$3y-y=6+2\\\\2y =8$

Dividing both side by 2 we get;

$\frac{2y}{2}=\frac{8}{2} \\\\y=4$

Now AB = $3y -2 =3\times 4-2 =12-2 =10$

Also

BC = AD

Substituting the value we get;

$x+12=2x-4$

Combining the like terms we get;

$2x-x=12+4\\\\x =16$

Now BC = $x+12 =16+12 =28$

Hence AB = 10 and BC =28.