The sum of the first and second sides of the triangle is 37 cm of the second and third sides of 41 cm of the first

The sum of the first and second sides of the triangle is 37 cm of the second and third sides of 41 cm of the first and third sides of 32, so is the perimeter of the triangle? What is the length of the second side of the trackball seat?

Let a, b and c be the first, second and third sides of the triangle, respectively.

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

a + b = 37;

b + c = 41;

a + c = 32.

Let’s add all three equations:

a + b + b + c + a + c = 37 + 41 + 32.

2a + 2b + 2c = 110.

Let’s take 2 out of the bracket:

2 (a + b + c) = 110.

Divide the equation by 2:

a + b + c = 55. Since (a + b + c) is the perimeter of the triangle (the perimeter is the sum of the lengths of all sides), the answer is: the perimeter of the triangle is 55 cm.

We find the length of the second side of the triangle using the expression for the perimeter and the last equation in the system:

a + b + c = 55; (a + c) + b = 55;

a + c = 32.

32 + b = 55; h = 55 – 32 = 23 (cm).

Answer: the perimeter of the triangle is 55 cm, the second side is 23 cm.