In triangle XYZ, the length of side XY is 29 mm and the length of side YZ is 43 mm. Which of the following could be the length of side XZ?
None of the above.
To determine the possible length of side XZ in triangle XYZ, 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 remaining side.
In this case, we have side XY = 29 mm and side YZ = 43 mm. Let's evaluate the possible length of side XZ using the triangle inequality theorem.
For side XZ to be a valid side length, it must satisfy the following condition:
XY + YZ > XZ
Substituting the given values:
29 + 43 > XZ
72 > XZ
Therefore, any value greater than 72 mm could be the length of side XZ in triangle XYZ.
To find the possible length of side XZ in triangle XYZ, we can use the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, side XY has a length of 29 mm and side YZ has a length of 43 mm. To find the possible length of side XZ, we need to check if the sum of these two sides is greater than XZ.
Let's calculate the sum of side XY and side YZ:
29 mm + 43 mm = 72 mm
Now, we can compare this sum to the possible lengths for side XZ. If the sum is greater than XZ, then the given length is possible. If the sum is equal to XZ, then it forms a degenerate triangle. If the sum is smaller than XZ, then the given length is not possible.
So, for the given lengths of XY and YZ, the possible lengths of XZ are:
- Any length greater than 72 mm, such as 73 mm, 80 mm, 100 mm, etc.
Note: It's important to remember that we are assuming this triangle is non-degenerate, which means it has a non-zero area, and the sides must meet the triangle inequality theorem.