Given two sides of a triangle (non-rectangular), one side is 37 mm, the other 43 mm. Find the perimeter of the triangle.

We denote by a one side of the triangle, by b the other, and by c the third. Let a = 37 (mm), b = 43 mm, side c is unknown.

Let’s use the property of a triangle: any side of a triangle is less than the sum of the other two sides, that is: c <b + a or c <43 (mm) + 37 (mm), c <80 (mm).

In this case, any side of the triangle is greater than the difference between the other two sides, that is: c> b – a or c> 43 (mm) – 37 (mm), c <6 (mm).

Third side c can range from 6 (mm) to 80 (mm) or 6 (mm) <c <80 (mm).

Calculate the perimeter of the triangle (the sum of all side lengths): P = a + b + c.

P = 37 (mm) + 43 (mm) + 6 (mm) = 86 (mm) or

P = 37 (mm) + 43 (mm) + 80 (mm) = 160 (mm).

The perimeter of a triangle can range from 86 (mm) to 160 (mm) or 86 (mm) <P <160 (mm).

Answer: 86 (mm) <P <160 (mm).