Question

Figure ABCD is a parallelogram.
What are the lengths of line segments AB and BC?
3
-2
в
• AB = 4, BC = 16
AB = 4; BC = 8
AB = 10; BC = 20
• AB = 10; BC = 28
y
+
6

Answer 1

Given:

Given that ABCD is a parallelogram.

The length of AB is 3y - 2.

The length of BC is x + 12.

The length of CD is y + 6.

The length of AD is 2x - 4.

We need to determine the length of AB and BC.

Value of y:

We know the property that opposite sides of a parallelogram are congruent, then, we have;

$AB=CD$

Substituting the values, we get;

$3y-2=y+6$

$2y-2=6$

     $2y=8$

       $y=4$

Thus, the value of y is 4.

Value of x:

We know the property that opposite sides of a parallelogram are congruent, then, we have;

$AD=BC$

Substituting the values, we get;

$2x-4=x+12$

 $x-4=12$

       $x=16$

Thus, the value of x is 16.

Length of AB:

The length of AB can be determined by substituting the value of y in the expression 3y - 2.

Thus, we have;

$AB=3(4)-2$

     $=12-2$

$AB=10$

Thus, the length of AB is 10 units.

Length of BC:

The length of BC can be determined by substituting the value of x in the expression x + 12.

Thus, we have;

$BC=16+12$

$BC=28$

Thus, the length of BC is 28 units.

Hence, the length of AB and BC are 10 units and 28 units respectively.