The perimeter of triangle ABC is 40 cm. Side BC is 5/7 of side AB, and side AC is 2 cm larger than AB. Find the AB side.

| September 5, 2021 | education

Let x denote the length of the side AB.

According to the condition of the problem, the length of the side BC of this triangle is 5/7 of the length of the side AB, and the side AC is 2 cm larger than AB, therefore, we can write the following relations:

| BC | = (5/7) * x;

| AC | = 2 + x.

By the statement of the problem, the perimeter of this triangle ABC is 40 cm.

The perimeter of any triangle is equal to the sum of the lengths of all three sides of this triangle, therefore, we can compose the following equation:

x + (5/7) * x + 2 + x = 40.

We solve the resulting equation:

2x + (5/7) * x + 2 = 40;

(19/7) * x + 2 = 40;

(19/7) * x = 40 – 2;

(19/7) * x = 38;

x = 38 / (19/7);

x = 38 * (7/19);

x = 7 * 38/19;

x = 7 * 2;

x = 14 cm.

Answer: The length of side AB is 14 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.