Question

what is the length of side ab of parallelogram abcd? units a 4q - 8 d c q + 4 b

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite sides are equal. So, $AB = CD$ and $AD=BC$. Here, assume $AB = 4q - 8$ and $CD=q + 4$. Set up the equation $4q-8=q + 4$.

Step2: Solve the equation for q

Subtract q from both sides: $4q - q-8=q - q+ 4$, which simplifies to $3q-8 = 4$. Then add 8 to both sides: $3q-8 + 8=4 + 8$, getting $3q=12$. Divide both sides by 3: $\frac{3q}{3}=\frac{12}{3}$, so $q = 4$.

Step3: Find the length of AB

Substitute $q = 4$ into the expression for $AB$ (which is $4q-8$). So, $AB=4\times4-8=16 - 8=8$.

Answer:

8