The perimeter of a quadrilateral is 62, one of its sides is 13, and the other is 17. Find the largest of the remaining

The perimeter of a quadrilateral is 62, one of its sides is 13, and the other is 17. Find the largest of the remaining sides of this quadrilateral if you know that you can inscribe a circle into it.

If a circle can be inscribed in a quadrangle, then the sums of the lengths of its opposite sides are equal. The perimeter of this quadrilateral is 62, which means that the sum of each of the pairs of opposite sides is equal to a half-perimeter, that is, 62/2 = 31. The sides known by the condition are adjacent, since the sum of their lengths is 13 + 17 = 30. Obviously, the largest of the remaining unknown sides is equal to the difference between the half-perimeter value and the length of the smaller of the known sides:
l = 31 – 13 = 18.