The sum of the lengths of the first triangle. The sides of the triangle are 33cm, the first and third are 39cm

The sum of the lengths of the first triangle. The sides of the triangle are 33cm, the first and third are 39cm, the second and third are 42cm. Find the perimeter of the triangle.

If we denote the length of the first side of the triangle as a cm, the second – b, and the third – c, then, in accordance with the condition, we can formulate three equations with three unknowns:

a + b = 33;

a + c = 39;

b + c = 42.

If we subtract the first from the second equation, then two equations with two unknowns remain:

c – b = 6;

b + c = 42.

The sum of the obtained equations is equal to:

2s = 48.

Where, c = 24 cm.

Accordingly, a = 39 – 24 = 15 cm, and b = 42 – 24 = 18 cm.

The perimeter of the triangle is a + b + c = 15 + 18 + 24 = 57 cm.