Determine if there is a triangle with a perimeter of 37 cm in which one of the sides is smaller

Determine if there is a triangle with a perimeter of 37 cm in which one of the sides is smaller than the other two by 2 cm and 11 cm.

Let x denote the length of the smaller side of such a triangle.

In the initial data for this task it is reported that this side is less than the other two sides of this triangle by 2 cm and 11 cm, therefore, the length of the other two sides of this triangle should be equal to x + 2 cm and x + 11 cm.

According to the condition of the problem, the sum of the lengths of all sides of a given one is 37 cm, therefore, we can draw up the following equation:

x + x + 2 + x + 11 = 37,

solving which, we get:

3x + 13 = 37;

3x = 37 – 13;

3x = 24;

x = 24/3 = 8 cm.

Find the lengths of the other two sides:

8 + 2 = 10 cm;

8 + 11 = 18 cm.

Since the sum of the lengths of the smaller sides of such a triangle, equal to 8 + 10 = 18 cm, turns out to be equal to the length of the third side of such a triangle, a triangle with such sides does not exist.

Answer: There is no triangle with such sides.