Answer:Let's analyze each set of side measurements:
1. -4, 8, 11
- To check if this set forms a right triangle, we square the lengths of the two shorter sides: (-4)^2 = 16 and 8^2 = 64.
- Then, we square the length of the longest side: 11^2 = 121.
- Next, we add the squares of the shorter sides: 16 + 64 = 80.
- Since 80 is not equal to 121, this set of side measurements cannot form a right triangle.
2. -6, 8, 13
- Squaring the lengths of the two shorter sides: (-6)^2 = 36 and 8^2 = 64.
- Squaring the length of the longest side: 13^2 = 169.
- Adding the squares of the shorter sides: 36 + 64 = 100.
- Since 100 is not equal to 169, this set of side measurements cannot form a right triangle.
3. √3, √5, 8
- Squaring the lengths of the two shorter sides: (√3)^2 = 3 and (√5)^2 = 5.
- Squaring the length of the longest side: 8^2 = 64.
- Adding the squares of the shorter sides: 3 + 5 = 8.
- Since 8 is not equal to 64, this set of side measurements cannot form a right triangle.
4. √3, √13, 4
- Squaring the lengths of the two shorter sides: (√3)^2 = 3 and (√13)^2 = 13.
- Squaring the length of the longest side: 4^2 = 16.
- Adding the squares of the shorter sides: 3 + 13 = 16.
- Since 16 is equal to 16, this set of side measurements can form a right triangle.
Therefore, the set of side measurements that can form a right triangle is √3, √13, 4.
Explanation: