Question

what is the length of side ab of parallelogram abcd?
□ units
the parallelogram abcd has side ab labeled as 4q - 8 and side dc labeled as q + 4 (from the image of the parallelogram).

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram, opposite sides are equal. So, \( AB = CD \).
Given \( AB = 4q - 8 \) and \( CD = q + 4 \), we set them equal: \( 4q - 8 = q + 4 \)

Step2: Solve for \( q \)

Subtract \( q \) from both sides: \( 4q - q - 8 = 4 \)
Simplify: \( 3q - 8 = 4 \)
Add 8 to both sides: \( 3q = 4 + 8 \)
\( 3q = 12 \)
Divide by 3: \( q = \frac{12}{3} = 4 \)

Step3: Find length of \( AB \)

Substitute \( q = 4 \) into \( AB = 4q - 8 \):
\( AB = 4(4) - 8 \)
\( AB = 16 - 8 = 8 \)

Answer:

8