Megan is jealous of her older sister's \(a\) x \(b\) inch Zac Efron poster, so she cuts out a rectangle around his face, which has dimensions \(\frac{a}{2}-2\) by \(\frac{b}{3} - 5\), and steals it. Megan's older sister decides she's over Zac Efron anyways, and uses the rest of the paper as wrapping paper. She wraps an \(11\) -inch cube, wasting no paper, and has \(3\) square inches leftover. If \(a\) and \(b\) are integers and \(b > a\), and the difference between the length and width of the poster is less than \(50\), find the dimensions of the poster. Express your answer as the ordered pair \((a, b)\).

Guest Dec 14, 2020