58 MN:NK:KL=2:6:7, P_MNKL=54, MN, NK, KL, LM-?

Let the sides be 2x, 6x, 7x, and y. The perimeter is 2x + 6x + 7x + y = 54, so 15x + y = 54. Since it's a tangential quadrilateral, opposite sides sum to the same value: 2x + 7x = 6x + y, which means 9x = 6x + y, so y = 3x. Substituting into the perimeter equation: 15x + 3x = 54, so 18x = 54, and x = 3. Thus, MN = 2*3 = 6, NK = 6*3 = 18, KL = 7*3 = 21, and LM = 3*3 = 9.