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 a 3y - 2 b 2x - 4 x + 12 d y + 6 c

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - sides are equal. So, $AB = DC$ and $AD = BC$.
We have $AB=3y - 2$ and $DC=y + 6$. Then $3y-2=y + 6$.
Solve for $y$:
$3y-y=6 + 2$
$2y=8$
$y = 4$.

Step2: Find length of $AB$

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

Step3: Use the other opposite - sides equality

We have $AD = 2x-4$ and $BC=x + 12$. Then $2x-4=x + 12$.
Solve for $x$:
$2x-x=12 + 4$
$x=16$.

Step4: Find length of $BC$

Substitute $x = 16$ into the expression for $BC$.
$BC=x + 12=16+12=28$.

Answer:

AB = 10; BC = 28