Final answer:
To find the length of RS in parallelogram ABCD, we can set up an equation using the given lengths of QR and QP. QR = 8x + 2, and QP = 4x - 6. By setting QR and QP equal to each other and solving for x, we find that x = -2. Substituting this value back into the expressions for QR and QP, we find that RS has a length of -14 units.
Step-by-step explanation:
To find the length of RS in parallelogram ABCD, we need to use the properties of parallelograms. In a parallelogram, opposite sides are equal in length. So, we can set up an equation using the given lengths of QR and QP:
QR = 8x + 2
QP = 4x - 6
Since QR and QP are opposite sides of the parallelogram, they must be equal. Setting them equal and solving for x:
8x + 2 = 4x - 6
4x = -8
x = -2
Now, we can substitute the value of x back into the expressions for QR and QP to find their lengths:
QR = 8(-2) + 2 = -14
QP = 4(-2) - 6 = -14
Since QR and QP have the same length, we know that RS must also have a length of -14 units.