1. **State the problem:** We have a quadrilateral □PQRS with perimeter 144 and the condition that PQ = QR. 2. **Define variables:** Let the length of PQ = QR = $x$. 3. **Express other sides:** Let the length of RS = SP = $y$ (since the problem implies pairs of equal sides). 4. **Write the perimeter equation:** The perimeter is the sum of all sides: $$PQ + QR + RS + SP = 144$$ Substitute the variables: $$x + x + y + y = 144$$ 5. **Simplify the equation:** $$2x + 2y = 144$$ Divide both sides by 2: $$\cancel{2}x + \cancel{2}y = \frac{144}{2}$$ $$x + y = 72$$ 6. **Find lengths of sides:** The problem does not provide more conditions to find unique values of $x$ and $y$, so the lengths are expressed in terms of each other: - Lengths of sides PQ and QR are $x$. - Lengths of sides RS and SP are $y = 72 - x$. **Final answer:** - PQ = QR = $x$ - RS = SP = $72 - x$