To determine the length of side QR in triangle PQR, we first need to establish some basic rules about triangles. Given that in any triangle, the sum of the lengths of any two sides must always be greater than the length of the third side, we can utilize this principle to analyze the options available.
Let’s look at each option systematically:
- Option 1: 8 units
- Option 2: 83 units
- Option 3: 16 units
- Option 4: 163 units
We know that two sides of a triangle must sum to be greater than the third. Since we are looking for the length of side QR, we should consider how the already known lengths would relate to each option.
However, without specific lengths given for sides PQ and PR, it’s challenging to unequivocally determine which of the options is valid. We will provide insights based on typical triangle properties.
1. **For 8 units:** This is a plausible length for QR, especially if PQ and PR are longer sides, since shorter lengths can effectively form valid triangles.
2. **For 83 units:** This length could also be possible if both other sides are significantly longer than 83 units, but it’s less commonly the case for typical triangles with smaller sides.
3. **For 16 units:** Like the 8 units, this is another reasonable choice, assuming PQ and PR offer sufficient length as well.
4. **For 163 units:** This option seems less likely unless the other two sides are extraordinarily long, which is often impractical in standard problems.
In conclusion, without further specific lengths for sides PQ and PR, we can’t definitively determine which of the multiple choices is correct. However, if we had to lean towards an estimate based on common scenarios, we might suggest that either 8 units or 16 units are the most feasible lengths for side QR in triangle PQR.