The sum of the lengths of the first and second sides of a triangle 50 centimeters the sum of the lengths

The sum of the lengths of the first and second sides of a triangle 50 centimeters the sum of the lengths of the second and third sides 52 centimeters the sum of the lengths of the first and third sides 58 centimeters Find the sides of this triangle?

Let us denote the lengths of the sides of this triangle by the letters a, b and c.

Then the condition of the problem can be written in the form of a system of three equations:

a + b = 50,

c + a = 58,

b + c = 52.

From the first equation we get:

b = 50 – a.

From the second equation we get:

c = 58 – a.

Substitute these values into the third equation:

b + c = 52,

50 – a + 58 – a = 52,

108 – 2 * a = 52,

2 * a = 56,

a = 56: 2,

a = 28 (cm).

Then b = 50 – 28 = 22 (cm) and c = 58 – 28 = 30 (cm).

Answer: 28 cm, 22 cm and 30 cm.