Question

using the parallelogram side theorem
what is the length of side ab of parallelogram abcd?
units

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, \(AB = CD\). Given \(AB=4q - 8\) and \(CD = q + 4\). Then we 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 \(3q-8 = 4\).
Add \(8\) to both sides: \(3q-8 + 8=4 + 8\), so \(3q=12\).
Divide both sides by \(3\): \(q=\frac{12}{3}=4\).

Step3: Find the length of \(AB\)

Substitute \(q = 4\) into the expression for \(AB\). \(AB=4q-8\), so \(AB=4\times4-8\).
First, calculate \(4\times4 = 16\), then \(16-8=8\).

Answer:

\(8\)