The perimeter of triangle ABC is 140 cm, the sum of sides AB and AC is 98 cm

The perimeter of triangle ABC is 140 cm, the sum of sides AB and AC is 98 cm, which is 21 more than the sum of sides AB and BC. Find the lengths of the sides of the triangle.

let AB = x, AC = y, then we find BC from the condition “the sum of the sides AB and AC is 98 cm, and the perimeter of the triangle ABC is 140 cm”, i.e. BC = 140-98 = 42
consider the following situation: x + 42 = 98 + 21, x = 119-42 = 77, i.e. AB = 77
and the remaining side of the AC is calculated from the perimeter: AC = 140-77-42 = 21
Answer: AB = 77, BC = 42, AC = 21