the lengths of 2 sides of a triangle are 2 inches and 10 inches. find the range of possible lengths for the third side, s.

s+2 >10 AND s+10>2 AND 2+10>s

s > 8 and s > -8 and s < 12

so s has to be between 8 and 12

makes sence now. thanks so much!

To find the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's denote the lengths of the two given sides as a = 2 inches and b = 10 inches. The inequality we need to consider is:

a + b > s

Substituting the given values, we have:

2 + 10 > s

12 > s

Therefore, the possible range of lengths for the third side, s, is any value greater than 12. In other words, s > 12.

To find the range of possible lengths for the third side of a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's denote the lengths of the two sides as a = 2 inches and b = 10 inches. Now we can apply the triangle inequality theorem:

a + b > s

Substituting the given values, we have:

2 inches + 10 inches > s

This simplifies to:

12 inches > s

Therefore, the length of the third side, s, must be less than 12 inches for a valid triangle.

In summary, the range of possible lengths for the third side, s, is 0 < s < 12 inches.