Since N is the midpoint of AC and O is the midpoint of BC, NO = ½AB.
Since M is the midpoint of AB, MB = NO = 15.
Therefore, AB = 2·MB = 30.
Since the perimeter of the triangle is 112 and AB = 30, AC + BC = 82.
Since AC2 + BC2 = AB2, AC2 + BC2 = 302 = 900
Since AC2 + BC2 = 900 ---> AC2 + 2·AC·BC + BC2 = 900 + 2·AC·BC
---> (AC + BC)2 = 2·AC·BC
Since AC + BC = 52, ---> (82)2 = 2·AC·BC
6724 = 2·AC·BC
Dividing by 4, 1681 = ½·AC·BC
But, ½·AC·BC is the area of triangle(ABC).