if two sides of a triangle are 8 feet and 15 feet the length of the third side could be?

The length of any two sides must be greater than the third side, x.

x+8>15 => x>7
x+15>8 => x>0
8+15>x => x<23
Therefore the third side must be between 7 and 23 feet, or
7<x<23

For a triangle, you are Given the two side lengths of 10ft and 22ft. what is the shortest possible length of the third side? What is the longest?

Well, according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, if the two sides of a triangle are 8 feet and 15 feet, the possible range of the length of the third side could be anything from 7 feet to 22 feet. Or, if you want a more humorous response, maybe it could be as long as a giraffe's neck or as short as a T-Rex's arms!

To determine the possible length of the third side of a triangle when two sides are known, 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 apply this to the given sides of the triangle:

Given:
Side 1 = 8 feet
Side 2 = 15 feet

Using the triangle inequality theorem, we can write the following inequality:

Side 1 + Side 2 > Side 3

Substituting the given values:

8 + 15 > Side 3

23 > Side 3

Therefore, the third side must be less than 23 feet in order for a triangle to be formed.

To find the possible length of the third side of a triangle when you know the lengths of the other two sides, you can use the Triangle Inequality Theorem.

According to the Triangle Inequality Theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

So, in this case, we have two sides with lengths 8 feet and 15 feet. To find the possible lengths for the third side, we can set up an inequality:

8 + 15 > x

Simplifying the inequality:

23 > x

Therefore, the length of the third side (x) must be less than 23 feet for a valid triangle. However, we also need to consider the other side length, which is 8 feet. So, the third side must satisfy the following inequality as well:

x + 8 > 15

Simplifying the inequality:

x > 7

Combining the two inequalities, we have:

7 < x < 23

Hence, the possible length for the third side could be any value between 7 feet and 23 feet.