Question

using the parallelogram side theorem
what is the length of side ab of parallelogram abcd?
units
(diagram: parallelogram abcd with side cd labeled ( q + 4 ) and side ab labeled ( 4q - 8 ))

Explanation:

Step1: Set sides equal (parallelogram)

In a parallelogram, opposite sides are equal. So, \( CD = AB \), which means \( q + 4 = 4q - 8 \).

Step2: Solve for \( q \)

Subtract \( q \) from both sides: \( 4 = 3q - 8 \).
Add 8 to both sides: \( 12 = 3q \).
Divide by 3: \( q = 4 \).

Step3: Find length of \( AB \)

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

Answer:

8