# The AB side of the ABC triangle is 7cm larger than the AC side, which is 6cm less from

The AB side of the ABC triangle is 7cm larger than the AC side, which is 6cm less from the BC side. find the sides of a triangle whose perimeter is 49cm

According to the terms of the assignment, firstly, the AB side of the ABC triangle is 7 cm larger than the AC side, that is, AB = AC + 7 cm.Secondly, the AC side is 6 cm less from the BC side, that is, AC = BC – 6 cm Let us substitute this expression for AC into the equality of the first condition: AB = BC – 6 cm + 7 cm = BC + 1 cm.
Thirdly, the perimeter of the triangle is 49 cm, that is, AB + AC + BC = 49 cm. Let’s substitute the found expressions for AB and AC into this equality. Then, we get: BC + 1 cm + BC – 6 cm + BC = 49 cm or 3 * BC = 49 cm – 1 cm + 6 cm = 54 cm, whence BC = (54 cm): 3 = 18 cm.
Let’s calculate the other sides: AB = 18 cm + 1 cm = 19 cm and AC = 18 cm – 6 cm = 12 cm.
Note that a triangle with sides AB = 19 cm, AC = 12 cm and BC = 18 cm satisfies the conditions for the existence of a triangle.
Answer: AB = 19 cm, AC = 12 cm and BC = 18 cm. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.