The sum of the lengths of the sides AB and BC of the triangle. ABC is 11 cm. The sum of the lengths

The sum of the lengths of the sides AB and BC of the triangle. ABC is 11 cm. The sum of the lengths of the sides BC and CA is 7 cm, and the sum of the lengths of the sides AB and CA is 8 cm. Find the perimeter of the ABC triangle Find the length of each side of this triangle.

According to the condition of the problem, we compose the equations:

AB + BC = 11; ( one )

AB + AC = 8; (2)

BC + AC = 7. (3)

The perimeter of a triangle is equal to the sum of the lengths of its sides, that is, in this problem:

P = AB + BC + AC. ( 4 )

In order to solve, we add equations (1), (2), (3):

AB + BC + AB + AC + BC + AC = 11 + 8 + 7;

2 * (AB + BC + AC) = 26.

We use (4) and find the perimeter:

P = 26/2 = 13.

Find side AB:

AB = (AB + BC + AC) – (BC + AC) = P – (BC + AC) = 13 – 7 = 6.

Similarly:

BC = 5; AC = 2.